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By L. E. Wilsey, R. A. Morse, P. L. Terwilliger, Howard N. Hall, P. M. Bridges

Theoretical and experimental investigations of a constant pressure gravity drainage system are reported. Experimental data are presented to show that recovery to gas breakthrough by gravity drainage is inversely proportional to rate. The gravity drainage reference rate, which is numerically equal to the so-called "maximum theoretical rate of gravity drainage" is shown to have no particular significance from a recovery standpoint. Before this rate can be used as a basis of comparison for recoveries, it is necessary that the relative permeability and capillary pressure characteristics and displacing fluid viscosities be identical for the systems compared. A method is presented by which accurate prediction of the performance of a gravity drainage system can be made. Close agreement between experimental and calculated drainage performance shows that steady state relative permeability and static capillary pressure data can be used to describe fluid displacement behavior. The very wide range of liquid recoveries before gas breakthrough which result from production rate variation alone demonstrates the importance of this factor in planning depletion of a gravity drainage reservoir. Calculated results are presented which show that little additional recovery can be expected from a high pressure gravity drainage system between the times of gas breakthrough and attainment of such high gas/liquid ratios as to make further pressure maintenance impractical. INTRODUCTION It bas been recognized for some time that gravity forces play an important part in the recovery of oil from some types of reservoirs. Field experience has shown that under certain conditions, gravity drainage can result in very high oil recov- eries. Qualitative reasoning has led most engineers to the general conclusions that: (1) Where gravity drainage is important, the reservoir pressure should be maintained by gas injection at the crest of the structure to prevent shrinkage of the oil in place and to keep a low viscosity so the oil can drain at the fastest possible rate. (2) Recovery by gravity drainage is rate sensitive. A survey of the literature indicates that while considerable work has been done on the effects of gravity in oil production problems, no satisfactory method of calculating the performance of gravity drainage reservoirs has been reported.1,2,3,4,5 In the absence of any proven method of calculating reservoir performance, the level at which pressure should be maintained and the rate of production for most efficient operation has been open to debate. The limits and general character of the recovery us rate relationships are apparent from the following: As rates of production approach zero, oil will drain by virtue of its own weight fast enough that the saturation distribution is always approximately the same as the original static capillary distribution. That is, at the gas-oil contact the liquid saturation goes from 100 per cent to a value of perhaps 10 to 30 per cent in a very short distance, so that as production continues. a relatively sharp gas-oil contact moves down-structure, leaving a very low residual oil saturation in the originally oil saturated zone. At very high rates of production, the oil that drains by virtue of its own weight is negligible and recovery will approach that of a horizontal gas drive, leaving a much higher residual oil saturation. At intermediate rates of production. recovery should be between these extreme*. Despite the lack of quantitative methods, tentative agreement had been reached on the question of optimum producing rate. It has been generally concluded that rather sharp decrease in recovery would occur at rates of production above the "maximum rate of gravity drainage" and hence this rate should not be exceeded. The "maximum rate of gravity drainage" is defined as the rate of production from a 100 per cent

Jan 1, 1951

The Naval Consulting Board is asking the aid of all the members of the Institute in its effort to help solve the submarine problem. Probably every member of the Institute has some suggestion, and while each one of these may be of only slight value in furnishing the remedy, the aggregate may be of great service. Every member of the Institute will soon receive a pamphlet known as Bulletin No. 1 of the Naval Consulting. Board of the United States in which full information and instructions will be given to all of those who are willing to assist. It is hoped when this information is received the members of the Institute will give it their prompt attention and write as soon as possible to the Secretary of the Naval Consulting Board, 13 Park Row, New York, N. Y.

Jan 9, 1917

The first production on the Island of Trinidad was discovered 29 years ago; 13,275 acres were proved for oil and gas to the end of 1937, and 145,076,700 bbl. was produced from 2661 wells, or 10,928 bbl per acre. The production of oil in 1936 was 13,237,030 bbl. and in 1937 a new peak of 15,498,350 bbl. was reached. During November 1937, the daily average production was 43,350 bbl., or 35 bbl. per well, while the maximum gas production was 45 million cubic feet daily. Two hundred fifty wells were completed during 1937 and 15 abandoned. At the end of last year, 800 wells had been temporarily shut down, 1235 were producing oil and gas, and 2 were producing gas only. Six hundred seventy-nine dry wells had been drilled to the end of 1937. At the end of November 1937, the following oil-producing methods were in use: 395 wells flowing, 491 pumping, 97 on air-gas lift and 252 wells miscellaneous. There were no flooding operations. The oil is produced from the Miocene and Eocene and is of both asphalt and paraffin base. The gas produced averaged approximately 1050 B.t.u. per cu. ft. with 0.8 gal. of gasoline per 1000 cubic feet.

Jan 1, 1938

By AIME AIME

MANY of the important papers to be presented at the World Congress of Engineering at Tokyo, in November, 1929, are being furnished by members of A.I.M.E. and a list of them is given below: "Fifty Years of Physical Metallurgy,,-by H. M. Boylston, Case School of Applied Science, Cleveland, Ohio.

Jan 1, 1929

By Marcus Grossmann

THIS paper offers for consideration certain somewhat radical modifications in the iron-carbon diagram, these modifications being the result of the presence of notable amounts of alloying elements. When only small amounts of alloys are present, 'the standard iron-carbon diagram (Fig. 1) can be used with but insignificant changes; when larger amounts of Chromium, Per Cent FIG. 1.-IRON-CARBON DIAGRAM. FIG. 2.-IRON-CHROMIUM DIAGRAM. alloys are present, however, it assumes a distinctly altered appearance. No comment is offered for the present except to call attention to the delta area, A4BM, which represents a region of mixtures of austenite and delta iron, just as area A3SP represents mixtures of austenite and alpha iron.

Jan 12, 1926

By S. P. Kinney, C. E. Wood, T. L. Joseph

In connection with its investigations of the blast-furnace process, the Bureau of Mines, in cooperation with the Minnesota School of Mines Experiment Station, developed a 6-ton experimental furnace. Such a furnace was needed to determine the feasibility of producing ferroman-ganese from Minnesota manganiferous iron ores, a problem of national importance because of the present need for manganese in the steel industry and our small reserves of ferro-grade ores. Furnace operators are reluctant to use new or untried raw materials or to make decided innovations in practice on account of the financial hazard of experimenting with full-scale equipment. A small furnace which can be operated at a relatively low cost is particularly adapted for testing new raw materials and for determining the feasibility of decided innovations in practice. Laboratory experiments, plus whatever information may be available, are valuable but often do not indicate the net result of changes in an operation involving a large number of interrelated variables. From time to time the cooperation of the Bureau of Mines is solicited in connection with problems involving departures from normal procedure. Under these circumstances some sort of a practical demonstration is a desirable forerunner to full-scale operations which appear feasible after small-scale tests. The Aluminum Co. of America was interested in knowing the practicability of smelting a charge of bauxite, iron ore, and limestone, of proportions that would produce slag of the following composition: A1203, 47 to 48 per cent.; CaO, 41 to 42 per cent.; SiO2,4 to 5 per cent.; TiO2, 2 to 3 per cent.; FeO, 1 percent., and MgO, 1.8 percent. In addition to determining whether it was feasible to operate a blast furnace on slag approaching the composition given above, a quantity of slag was needed for a series of experiments that would show the relative ease and cost of extracting alumina from slag which could be made in the blast furnace, as compared to extracting it from raw bauxite. The value of the slag as a raw material

By M. Prats, D. G. Russell

The performance of a well in a bounded, layered reservoir with interlayer crossflow has been investigated mathematically. The system studied comprises a centrally located well in a bounded cylindrical reservoir composed of two layers of contrasting physical properties. The reservoir contains a single fluid of small and constant compressibility. In the case of a well producing at constant pressure, the production rate of the crossflow system declines exponentially after the early transient behavior dies out. For wells which produce with constant rate, the pressure-time relationship is linear following the transient. For very early production time, the production rate of the two-layer crossflow system behaves as that of the two-layer stratified system (the case in which the layers are in communication at the well only). Except for early time, in most practical cases the performance of a two-layer reservoir with cross-flow can be duplicated by that of a single-layer reservoir. The equivalent single-layer reservoir must have the same pore volume and the same drainage and wellbore radii as in the two-layer case. In addition, the equivalent reservoir must have a "kh" (permeability x thickness) product equal to the sum of the "kh" products of the respective layers in the crossflow system. If the porosity and permeability distributions are known, the production and pressure behavior of a well with and without crossflow can be predicted. From a comparison of the observed pressure or production performance of a well and the theoretical behavior, the occurrence of interlayer crossflow can be detected. INTRODUCTION When flow is possible across the bedding plane from a low-permeability layer into an adjacent layer of moderate or high permeability, the earlier depletion of the more permeable layer will cause such flow to occur. If this situation exists, the oil recovery from tight layers can be appreciable; thus, the economic ramifications of interlayer crossflow are apparent. The possible importance and extent of flow between adjacent and connected layers — whether resulting from capillary, gravitational, or viscous forces — have been the subject of considerable speculation for many years. Jacquard1 presented a rigorous analysis of the crossflow due to single-fluid expansion occurring between two adjacent and connected layers when the well produces at constant rate. His presentation was entirely mathematical, however, and no numerical results from evaluation of the mathematical solutions were presented. Our objectives in the preparation and presentation of the present paper are essentially twofold— (1) to analyze the behavior of a well which produces a single compressible fluid from a bounded, layered reservoir with interlayer crossflow, and (2) to present practical numerical results and simplified formulas to facilitate engineering analysis of reservoirs with crossflow. The constant-terminal-pressure case was analyzed rigorously, whereas the constant-terminal-rate case was treated only for semisteady-state conditions. DESCRIPTION OF THE IDEALIZED TWO-LAYER RESERVOIR The reservoir to be studied is assumed to be bounded and cylindrical in shape, with a completely penetrating well at its center. The reservoir is composed of two adjacent horizontal layers between which fluid is free to flow. Each layer is assumed to be homogeneous, isotropic and completely filled with a fluid of small and constant compressibility. The total thickness of the reservoir is small enough

By J. L. Huitt, B. B. McGlothlin, D. K. Lowe

Published correlations for the principal aspects of hydraulic fracturing were combined into a digital computer program to facilitate the study of interrelated variables. The computer program includes individual relationships for fracture width during pumping, fracture area generated, propping agent embedment, flow capacities of propped fractures and transport of propping agents in horizontal fractures. The effects of more than 20 treatment and formation parameters on the predicted results of hydraulic fracturing treatments were studied. The effects of these parameters were determined for (I) fracture width during injection, (2) fracture width after the overburden comes to rest on the propping agents, assumed not to be crushed, (3) generated and propped fracture area, (4) location and concentration of propping agents in the fracture when injection ceases, (5) flow capacities of the various propped sections of the fracture and (6) expected increase in the well productivity. The effects of propping agent, formation and fracturing fluid parameters on well productivity are discussed. The parameters that were found to have the most pronounced effects on hydraulic fracturing treat~nents are injection rate, treatment volume, fracturing fluid coefficient, size and amount of propping agent, spearhead volume, well drainage radius and formation capacity. INTRODUCTION Many correlations have been published for predicting effects of various parameters that are considered in the design of hydraulic fracturing treatments. The Carter equation' can be used to predict generated fracture radius as a function of fracture width, fracturing fluid leakoff and other parameters. Fracture width can be determined by use of the Perkins and Kern correlation' in which the fracture width is related to the fracture radius, fluid injection rate and certain formation and fracturing fluid parameters. Wahl and Lowe et aL4 have reported methods of predicting the location of propping agents in fractures when pumping ceases. The former study is applicable to the case where the ratio of propping agent diameter to fracture width is less than 0.1. The latter is applicable when this ratio is greater than 0.1. These studies showed that the propping agent placement in horizontal-radial fractures depends principally on how the individual particles are transported in the fracture by the carrying fluid. Particle transport in fractures is determined by local fluid velocity in the fracture, fluid and particle properties, and the size of the particle relative to the fracture width. The distribution of propping agents, effective overburden pressure and formation rock strength control the propped fracture width6 by controlling the extent to which the propping agent particles embed into the fracture faces. From the distribution of propping agents and the propped fracture width, fracture flow capacities can be calculated or the various regions of the fracture. The flow capacities and the radial extent of these regions can be combined with reservoir information to predict the productivity increases for fractured wells. In all these studies, the effects of certain treatment and/ or reservoir parameters on one facet of fracturing can be predicted only if other facets which the parameters affect are fixed. For instance, fracture width and radius are interrelated; that is, to calculate the value of one, the value of the other must be known. Also, some parameters influence more than one aspect of fracturing. For example, prop-pant transport is a function of both fracture width and fluid viscosity. but fracture width is itself a function of fluid viscosity. Since these calculations are complex and the parameters interrelated, it is not possible to write an equation with which the over-all effects of treatment parameters can be solved explicitly. For these reasons, the correlations for determining the effects of the parameters which are most significant in hydraulic fracturing treatments have been incorporated into a digital computer program. COMPUTER PROGRAM The program, which was written for an IBM 7094 computer, can be used to predict results of most of the combinations and values for the treatment parameters that are ordinarily considered for fracturing treatments. A spearhead of fracturing fluid and a propping agent-carrying fluid with different fluid properties can be taken into account. Also, the total volumes and relative amounts of the spearhead and carrying fluids can be varied. Two different propping agents (as used in tail-in operations) and a wide range of formation properties and injection rates are considered. The computer program (Fig. 12) consists of several sets of calculations. First, the final flooded fracture radius and average fracture width at the cessation of pumping are calculated. This is done by simultaneous solution of the Perkins and Kern fracture width equation and the Carter equation for flooded fracture radius (equations used in the computer program appear in the Appendix). The next step is to determine local fluid velocity in the fracture as a function of time and radius. Since it is not possible to write this function in closed form expression, a table of velocity values is generated by the program and stored for subsequent use. The time span from the beginning of

By Thomas C. Wilder, Walter E. Galin

Measurements of the electromotive force of the cell at 995°C have shown that the cell may be used to detennine the zinc content of molten Cu-Zn alloys to the nearest 0.05 wt pct. The cell is used for brass melts to which no ZnO is added intentionally, because essentially all oxygen in the Cu-Zn-O system is present in the form of ZnO. The cell is also used to detev,nine the thernodynamic activity of zinc for Cu-Zn al1oys of the brass composition range, from which the equilibrium partial pressure of zinc for such alloy may also be calculated. The electrochemical measurement of the concentration of the most active metal in other engneering- alloy systems by a similar technique is also considered. IN recent years there have been many studies concerning the direct electrochemical measurement of oxygen content in molten engineering metals.' These investigations employ galvanic cells in which the electrolytes are various solid mixed-oxides which conduct current by movement of oxide ion vacancies under the influence of an oxygen potential gradient. Similar cells have also been used to measure the thermodynamic properties of mixing of solid alloys,' one component of which has a much greater affinity for oxygen than the other component(s). One alloy system of obvious engineering importance comprised of two metals of greatly differing affinity for oxygen is copper-zinc. At the casting temperature of molten brasses, the zinc concentration is very difficult to control not only because its vapor pressure is very high, but also because of its high affinity for oxygen to form ZnO. Inasmuch as brass castings may be required to have a zinc concentration within very narrow limits, it would be advantageous for the brass industry to have a means for quickly measuring the zinc content in the molten alloy just prior to pouring. A calculation based on earlier thermodynamic studies of oxygen and zinc in dilute solution in binary Cu-O and CU-Z' alloys indicates that the oxygen concentration of molten 70 wt pct Cu-30 wt pct Zn brass must be much less than 1 ppm for the separate phase ZnO not to exist in the ternary Cu-Zn-O system. Thus it can be assumed that all molten brasses, both in the laboratory and in the foundry, are sufficiently saturated with oxygen for the separate phase ZnO to be present. In view of the foregoing reasons, the cell investigated at 995°C for the purpose of measuring the zinc concentration in molten copper-zinc alloys, particularly those of brass compositions. In this cell the left hand electrode is a reference electrode comprised of a mixture of the pure powders of nickel and nickel oxide, to which a platinum contact is made. The electrode of interest is a molten Cu-Zn alloy of unknown zinc concentration with a tantalum wire contact. The electrolyte is the commercially available (Zircoa) calcia stabilized zirconia. The ZnO in the Cu-Zn electrode compartment is not intentionally added, but is naturally present as a result of the infinitesimal amount of oxygen required for its formation in this alloy system. In cell [A] nickel oxide is reduced at the cathode where O= represents the electrolyte. At the anode dissolved zinc of the Cu-Zn alloy is oxidized to form ZnO(s) in its standard state Thus the overall reaction is for which the molar free energy change is where 5 is the Faraday equivalent (23,063 cal per v equivalent), is the electromotive force of the cell in volts after correction for the Pt-Ta thermocouple, FOf (ZO) and AFF (NO) are the standard molar free energies of formation of the respective oxides, and a2n is the thermodynamic activity of zinc in the molten Cu-Zn alloy. The reference state of zinc in this case is taken to be the pure liquid. At constant temperature all the terms of Eq. [I] are constant except and azn Thus since all other participants in the electrochemical reaction are in their standard states, the change in the electromotive force of Cell [A] is represented only by a change of the thermodynamic activity of zinc at constant temperature. The zinc concentration is related to the activity by sampling the alloy for chemical analysis after cell measurements are taken. EXPERIMENTAL A typical cell construction is shown in Fig. 1. This and other experimental details were similar to that described earlier with the exception of some minor modifications which are detailed below.

Jan 1, 1970

By R. F. Mehl, B. Lustman

THE formation of intermediate phase layers in cementation processes has been subjected to extensive qualitative investigation though to relatively little quantitative study; this work has recently been fully summarized by F. N. Rhines.1 It is necessary here only to enumerate the general conclusions drawn concerning the kinetic laws governing the growth of intermediate layers and to state what is known concerning the structural changes accompanying the generation of phase layers. I. When the intermediate phase is protective in type-i.e., when its density is less than that of the base metal, so that a continuous coating is formed and maintained the isothermal growth of the phase follows a simple parabolic equation: X2 = kt [I] where X is the thickness of the alloy layer, k the reaction rate constant, and t the time. The applicability of this equation to diffusion processes is tested by plotting the square of the thickness versus time, or by plotting the thickness versus the square root of time; the resultant achievement of a straight line in such. a plot has been con¬sidered sufficient proof of the validity of this equation. Exceptions have been found where liquid phases are involved in the reaction, where the diffusion layer is cracked,2 and where thin semimetallic oxide and sulphide coatings are formed on metals.3 In the first two cases the thickness increases linearly with time, and in the latter it is a logarithmic function of time. 2. The rate of thickening varies with temperature according to the Arrhenius equation k = Ae-Q/RT [2] where k is the parabolic rate constant of Eq. I, or some other rate-descriptive function, A is the action constant, e the base of natural logarithms, Q the heat of activation, R the gas constant, and T absolute temperature. This equation has been found to be generally valid except when transformations occur during reaction in either the base metal or in the reaction layer; in such instances Eq. 2 is still applicable with different values for the constants A and Q above and below the transformation temperature. 3. All phases that are stable at the temperature at which diffusion occurs will appear in the interdiffusion of two components. In some cases certain of the phases may be too thin to be observed and identified easily. Nonequilibrium phases have never been noted in thick reaction layers; i.e., layers of a thickness that may be discerned microscopically. The relative, thickness of each phase in a diffusion layer is proportional to the concentration gradient and to the rate of diffusion in that phase .4 The reaction layers tend to have a

Jan 1, 1942

By A. U. Seybolt

The pressure-temperature relations required to maintain the existence of Si3N4 in silicon-iron of 0.44-11.7 pet Si have been partially explored. The critical data obtained have allowed the calculation of some thermodynamic quantities, and have shown evidence of an order-disorder two-phase field extending at 800°C from about l pet to 5.5 pet Si. THE presence of silicon nitride in electrical sheet, nominally about 3 1/4 pet silicon, balance iron, has been described by several authors'" but there has been some discrepancy among them regarding the identity of the nitride. Also, little has been reported on the quantitative thermodynamic prop- erties. In the work to be reported here, the nitride has been found to be more stable than described by Corney and Turkdogan." Several silicon nitrides have been described in the past, including SiN, Si3N4 and Si2N4 (see, for example, Abegg6 and Pascal7). However, the literature on nitrides other than Si,N, is all very old. No recent investigators using the more powerful tools available today have reported the presence of any nitride other than S3,N4. W. B. Hicke and L. R. Brantley8 in 1930 determined the dissociation pressure of Si3N4 which they made by reacting nitrogen

Jan 1, 1959

By A. J. Williams

THE province of Saskatchewan, situated in the center of the Great Plains region of Canada, has, like most prairie areas, an essentially agricultural economy. Most of its population of about 860,000 is located in the southern half of the province in the farming and ranching areas. To the north of the prairie is a broad forested belt supporting a considerable timbering industry, and the northern one third of the province is glaciated pre-Cambrian rock formation. This latter area is, relatively barren of vegetation, but the presence within it of a considerable variety of radioactive, noble and base metals, and industrial minerals has been shown by prospecting in recent years.1 Glacial Geology The Keewatin ice sheet, considered to have accumulated in the country to the west of Hudson Bay in Pleistocene time, covered at its maximum advancement almost all of Saskatchewan and extended south of the international boundary. Only in the Cypress Hills in the southwest and around Wood Mountain in the south central portion of the province did the preglacial formations escape the action for this glacial period. The bedrock of the plains and forest areas therefore is overlain by moraines and modified glacial drift, which vary in thickness from a few feet to 400 or 500 ft.2 Glacial action in the pre-Cambrian area of the province was largely erosional, most of the more recent formations and some of the pre-Cambrian rock being transported out of the area to the south and west. It has been estimated that about 13 pct of this area is composed of lakes and rivers not too adaptable to rail or water transportation, so that until the use of aviation for exploration purposes became general; development of the area was slow. To the south, the heavy. mantle of glacial drift has to some extent deterred the discovery of industrial minerals in the bedrock underlying the forest and prairie regions.3 At the same time, this drift contains numerous deposits of those most elementary and necessary industrial minerals, sand and gravel. Sedimentary Basin The major feature of the sedimentary deposits underlying the plains regions is the basinal structure known as the Moose Jaw syncline, which runs from the southeast corner of the province in a northwesterly direction. To the west. of this syncline the formations curve upward, then have been faulted and further upthrust to appear at the surface in the foothills of-the Rockies in Alberta; to the east and north they curve upward into Manitoba and northern Saskatchewan, but the surface contacts are covered mostly with glacial drift.2,3 The axis of the syncline dips to thee southeast, so that there is also an upward trend of the formations along the axis to the northwest. In illustration of the regional structure underlying the province, the pre-Cambrian basement has been logged in drillholes at the following depths in several locations: Ogema (south central), 9390 ft; Gronlid (northeast), 2599 ft; Vera (northwest), 4422 ft; Big River (north northwest), 2348 ft. Fig. 1 indicates the general surface geology of the province, ignoring such glacial overburden as may overlie many of the bedrock formations. Also indicated is the approximate location of the axis of the Moose Jaw syncline.4 Industrial Minerals Clays: The province is fortunate in possessing a widespread distribution of clays of ceramic value, ranging from those used for heavy structural products to the high grade pottery and china clays. Shales suitable for brick and tile production are found in the Upper Cretaceous and Tertiary formations across the south of the province where the glacial drift is thin or nonexistent. Many deposits of glacial lake clays suitable for such wares are found scattered over the rest of the province south of the pre-Cambrian area. The Whitemud formation of the Upper Cretaceous is a narrow sedimentary, band of secondary clays found intermittently, at points, across the, south of the province where glacial action did not disturb or remove them.8 In the southwest corner of the province, around Eastend in the Frenchman River valley, the refractory clays of this formation are contaminated somewhat with iron compounds or other alteration products of basaltic rocks. This eliminates the use of those clays in true whitewares, as they fire to creamy buff shades at the lower temperatures and to a blue-specked grey at cone 8 to 12, (2280°F to. 2390°F), the range commonly used in firing whiteware. However, for use in the production of colored artware, caneware, stoneware or crockery, and sewerpipe, this type of clay makes an excellent body that requires little or no addition of flint, feldspar, or other fluxing materials such as are required in the higher class of ware.9 It is not a grade of clay that can be shipped great distances to the manufacturing centers, but a market for considerable tonnages has developed at nearby Medicine Hat, where cheap natural gas is available for the firing of the ware. Farther east in the south central portion of the province, the clays of the Whitemud formation are generally more refractory and white burning. The formation is divided into three zones, consisting of white clays, brown shale, and white sandy clays.

Jan 1, 1952

By D. A. Belforti, M. P. Lepie

Spectroscopically pure copper was melted on sapphire plaques in a zydrogen atmosphere. The surface tension of the liquid metal was determined using the sessile drop technique. Measurements were made by direct observation with the aid of a specially const,mcted telescope. The value obtained, 1268 dynes per cm, is compared to that found in the literature. THERE is at this time considerable interest in the use of ceramics for vacuum tubes. The crystalline material is superior to the more conventional glass in mechanical strength, chemical inertness, dielectric properties, ability to withstand high temperatures, and so forth. However, ceramics are much more difficult to seal hermetically with metals than are the glasses. For this reason an investigation was undertaken to determine the wetting and adhesion of metals to ceramics. The sessile drop technique offers a convenient means at elevated temperatures for measuring liquid surface tension, wetting angle, density, spread- ing coefficient, and work of adhesion. Thus, from the contour of a drop of liquid at rest on a solid surface one can obtain a quantitative evaluation of the degree to which the two substances will bond. To this end a special apparatus was constructed so that various molten metals could be observed. Standardization of the apparatus was done initially by measuring the surface tension of copper since this is well documented in the metallurgy literature. Although there are many methods available for the measurement of surface energy,'+ the sessile drop technique has been used most extensively for molten metals and ceramics.5"' Fig. 1 illustrates the dimensions to be measured. From these values, the surface tension of the liquid can be obtained using the Bashforth and bdams' equation and tables.

Jan 1, 1963

By M. Cohen, R. T. Howard

It has long been realized among metallurgists that a fast, reliable method for the quantitative determination of the percentage of microconstituents in an alloy would be of great benefit in studies of equilibrium and transformation in the solid state. For example, Polushkinl has shown that the compositions of two coexisting phases in a binary system at a given temperature may be calculated very simply with the aid of two alloys lying in the two-phase field if the relative amounts of the two phases in each alloy can be determined. Recently, Grange and Stewart2 have traced the course of the austenite-martensite reaction in a series of commercial steels by making visual estimates of the percentage of martensite formed as a function of cooling temperature. The correlation of mechanical properties with structure, a subject of wide-spread current interest, is likewise dependent upon quantitative microanaly-sis. Yet, there are very few investigations described in the metallurgical literature, wherein methods of quantitative microscopy are employed. Usually, the relative amounts of the microconstituents are estimated in a qualitative or semiquantita-tive way. The authors were faced with this problem some time ago in studying the kinetics of austenite decomposition. Several aspects of this research could not be treated satisfactorily by other quantitative tools, such as specific volume,' magnetic,6 dila-tometric, electrical resistance7 or x-ray measurements.a It became necessary to find an impersonal quantitative method that could be applied to microstructures. Fortunately, it was noted that geologists and petrographers had coped with quantitative microscopy to a considerable degree in their attempts to evaluate the mineral contents of rocks. A number of excellent articles were found on this subject, and since they appear to be unknown generally to many metallurgists, the first part of the present paper is concerned with a review of the literature in some detail. With this survey as a background, the authors have adapted the so-called methods of point-counting and lineal analysis to metallography, as described in the second part of the paper. Austenite-martensite structures were selected for illustration not only because they are important in many ways, but because such fine intermixtures are notoriously difficult to estimate visually. Literature Survey Perhaps the earliest work on quantitative microscopic analysis goes back to Delesse9 (1848) who proved mathemati-

Jan 1, 1948

By M. Cohen, R. T. Howard

It has long been realized among metallurgists that a fast, reliable method for the quantitative determination of the percentage of microconstituents in an alloy would be of great benefit in studies of equilibrium and transformation in the solid state. For example, Polushkinl has shown that the compositions of two coexisting phases in a binary system at a given temperature may be calculated very simply with the aid of two alloys lying in the two-phase field if the relative amounts of the two phases in each alloy can be determined. Recently, Grange and Stewart2 have traced the course of the austenite-martensite reaction in a series of commercial steels by making visual estimates of the percentage of martensite formed as a function of cooling temperature. The correlation of mechanical properties with structure, a subject of wide-spread current interest, is likewise dependent upon quantitative microanaly-sis. Yet, there are very few investigations described in the metallurgical literature, wherein methods of quantitative microscopy are employed. Usually, the relative amounts of the microconstituents are estimated in a qualitative or semiquantita-tive way. The authors were faced with this problem some time ago in studying the kinetics of austenite decomposition. Several aspects of this research could not be treated satisfactorily by other quantitative tools, such as specific volume,' magnetic,6 dila-tometric, electrical resistance7 or x-ray measurements.a It became necessary to find an impersonal quantitative method that could be applied to microstructures. Fortunately, it was noted that geologists and petrographers had coped with quantitative microscopy to a considerable degree in their attempts to evaluate the mineral contents of rocks. A number of excellent articles were found on this subject, and since they appear to be unknown generally to many metallurgists, the first part of the present paper is concerned with a review of the literature in some detail. With this survey as a background, the authors have adapted the so-called methods of point-counting and lineal analysis to metallography, as described in the second part of the paper. Austenite-martensite structures were selected for illustration not only because they are important in many ways, but because such fine intermixtures are notoriously difficult to estimate visually. Literature Survey Perhaps the earliest work on quantitative microscopic analysis goes back to Delesse9 (1848) who proved mathemati-

Jan 1, 1948

By L.W. Eastwood, Arthur E. Bousu, C. T. Eddy

The recrystallization and grain-growth phenomena of cold-worked metals have considerable industrial importance because of their role in the fabrication of metals. For this reason, and because of the general academic interest in the subject, these processes have received considerable attention since the time of J. E. Stead's paper1 on The Crystalline Structure of Iron and Steel. There are considerable differences of opinion regarding the theory of recrystallization and grain growth and also differences in the observation of the modus operandi of the processes themselves. The value of many of the existing quantitative data on grain growth is decreased by the failure to distinguish between the grain sizes just after complete recrystallization and those resulting from coalescence. For this reason also, the value of the diagrams of stable grain sizes, like those produced by Bass and Glocker2 and Czochralski3, is lessened in so far as an interpretation of the facts of recrystallization is concerned. It is hoped that the data presentcd in this paper will help to clarify and to simplify the facts relating to recrystallization, and at the same time will show that some of the present-day conceptions are untenable. A paper on the theory of recrystallization, with additional data, will be completed in the near future by the writers. Since the literature on the subject has been adequately and frequently reviewed, the only referenccs to it in this paper will be those necessary in the discussion of the data presented.

Jan 1, 1935

By Arthur E. Bousu, C. T. Eddy, L. W. Eastwood

The recrystallization and grain-growth phenomena of cold-worked metals have considerable industrial importance because of their role in the fabrication of metals. For this reason, and because of the general academic interest in the subject, these processes have received considerable attention since the time of J. E. Stead's paper1 on The Crystalline Structure of Iron and Steel. There are considerable differences of opinion regarding the theory of recrystallization and grain growth and also differences in the observation of the modus operandi of the processes themselves. The value of many of the existing quantitative data on grain growth is decreased by the failure to distinguish between the grain sizes just after complete recrystallization and those resulting from coalescence. For this reason also, the value of the diagrams of stable grain sizes, like those produced by Bass and Glocker2 and Czochralski3, is lessened in so far as an interpretation of the facts of recrystallization is concerned. It is hoped that the data presentcd in this paper will help to clarify and to simplify the facts relating to recrystallization, and at the same time will show that some of the present-day conceptions are untenable. A paper on the theory of recrystallization, with additional data, will be completed in the near future by the writers. Since the literature on the subject has been adequately and frequently reviewed, the only referenccs to it in this paper will be those necessary in the discussion of the data presented.

Jan 1, 1935

By J. F. Smith

ELASTIC constants of yttrium and eleven of the rare earth elements have been measured. This has been accomplished by measuring the propagation velocities of ultrasonic pulses. The velocity measurements were made by noting the elapsed time between an applied pulse and the appearance of successive echoes. The pulse-echo technique has become relatively common, and the basis of the measurement is outlined in several standard tests, e.g., Heuter and Bolt.1 Two important assumptions are made when using this method for the determination of elastic moduli. First, the pulse is assumed to propagate as a plane wave. To justify this assumption, the cross section of the test specimen should be large compared to the wave length of the transmitted pulse. For these measurements on the rare earth elements the minimum cross section wave length ratio was about 20. A second assumption which must be made when using polycrystalline specimens is that the grains are sufficiently numerous and randomly oriented so that the specimen may be approximated as elasti-cally isotopic. The grain size in the as-cast specimens which were used is believed to be sufficiently fine for this approximation, and the degree of preferred orientation is believed to be small. Supporting this viewpoint is the fact that elasticity measurements by the pulse-echo technique on as-cast specimens of other metals give results which are in satisfactory agreement with values obtained by other techniques. Hence, it is believed that the measured elasticity values for the rare earth elements are not apt to be seriously in error due to the assumption of elastic isotopy. The apparatus used in this determination was a modified Sperry Reflectoscope with a precisely calibrated time base circuit. Piezoelectric transducers were used both to generate the pulse and to detect the echoes. X-cut quartz crystals were used for the longitudinal modes, and Y-cut quartz crystals were used for the shear modes. Frequencies of 2.25 and 5 megacycles per sec were employed. Most of the specimens were 2.5 to 5.0 cm in length. Results Table I is a tabulation of the measured propagation velocities of longitudinal waves and of shear waves, together with densities obtained by Sped- ding, Daane, and Herrmann2 from lattice parameter measurements. The shear modulus, Poisson's ratio, and Young's modulus were calculated from the data in Table I through use of the following relationships: µ = pv32 [1] s=2-(vb/vs)2/2[1-(vb/vs)2] [2] and Y= 2µ(l+s) [3] where s is the shear modulus, Y is the Young's modulus, s is Poisson's ratio, p is the density, V0 is the longitudinal wave velocity, and v, is the shear wave velocity. The calculated quantities are shown in Table 11. Compressibility values can be computed from the relationship and the computed values may be compared with measured values obtained by Bridgman.8 Table III lists the data for such a comparison. The agreement is satisfactory, being particularly good for neodymi- um and gadolinium, poor for samarium, and intermediate for the other elements. Some variation is expected since Bridgman's measurements are isothermal, whereas the present measurements are adiabatic. In addition there may be some effect due to small variations in purity. Though most of the rare earth metals measured by Bridgman and all of the metals used in the present measurements were prepared at this laboratory, minor purity variations might exist since the samples came from different lots. Also, any imperfections such as dislocations, vacancies, voids, grain boundaries, microcracks, etc., should contribute to the volume change of a com-

Jan 1, 1958

By R. W. Gurry

IN the course of a series of measurements of the rate of diffusion of carbon in austenite at about 960°C. (1760°F.) and 1110°C. (2030°F.), it became necessary to determine carbon concentration when austenite is saturated with graphite, because of indications that the hitherto accepted value of the solubility of graphite in this temperature range is too low. Specimens of carbonyl iron were saturated at temperature in a hydrogen-toluene atmosphere which was in equilibrium with graphite. The carbon content of the steel was measured either by combustion or by the loss of weight after substantially complete decarburization in an atmosphere of hydrogen saturated at room temperature with water vapor. The absence of carbide or graphite as a phase at temperature was demonstrated by microscopic examination of saturated specimens that had been drastically quenched. The mean result of concordant measurements is that gamma iron saturated with respect to graphite contains 1.39 per cent carbon at 957°C. (1755°F.) and 1.89 per cent at 1110°C. (2030°F.). These two values, plotted along with what appears from the literature to be the best value (0.69 per cent) at the iron-graphite eutectoid temperature (738°C. or 1360°F.), yield a curve that is almost linear, and which, continued upward through a short interval, leads to a limiting solubility of 1.98 per cent at the iron-graphite eutectic temperature 1135°C. (2075°F.) instead of the commonly accepted value of about 1.7 per cent. EXPERIMENTAL PROCEDURE The samples of carbonyl iron, with the exception of those for microscopic examination, were cylinders 3.8 cm. long, 0.475 cm. in diameter. They were placed in a graphite holder and suspended in a vertical furnace, the temperature of which was controlled precisely by means of the resistance of the platinum winding.1 In the empty furnace the range of temperature over a distance of 4 cm. at the heat center was 9°C. (16°F.) but at a given location the temperature remained within ±0.5°C. (0.9°F.); it was measured by inserting a platinum-rhodium couple calibrated at the melting point of palladium, 1555°C. Since the presence of the sample probably improved the uniformity of temperature, it was decided to consider the average temperature of the sample to be 3°C. lower than the maximum measured in the empty furnace with the same setting of the controller. Data were obtained in the vicinity of two temperatures, 960°C. (1760°F.) and 1110°C. (2030°F.). The samples for microscopic examination, 2.2 cm. long, 0.475 cm. in diameter, were suspended individually on pure iron wire; for these no temperature correction was applied. The carburizing gas passed into the furnace was dry, oxygen-free hydrogen saturated at room temperature with

Jan 1, 1942

By M. G. Fowler

A GENERAL decline in copper production for most American producers occurred during the past year as a result of shortage in available labor. Few noteworthy technical developments have been reported; undoubtedly, many changes and improvements have been made but have not been reported because of lack of time. During the war years through 1944 the pressure for sustained high production has been of prime importance and during 1945, with slackening of production, many operators were faced with the problem of catching up on repairs and maintenance of plants, with inadequate labor supply. In hydrometallurgy there were some important developments that undoubtedly will be reported during 1946. Several operators in the Southwest have instituted experimental leaching programs to exploit low-grade oxidized and mixed ore bodies. The Bureau of Mines is conducting pilot-plant experimental work to determine the possibility of producing a satisfactory sponge iron at an attractive cost from deposits of iron ore and coal in Arizona. The sponge iron would be used for the production of cement cop¬per. The cell house of the Inspiration Consolidated Copper Co. at Inspiration,

Jan 1, 1946