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By T. V. Moore

IN many of the important problems of the petroleum engineer, it is necessary to know accurately the laws governing the flow of gas and liquid mixtures in vertical' pipes. Although much work has been done along these lines, no satisfactory solution to the problem has been found. A good theoretical discussion of the energy balance in a gas¬lift has been published-by Versluys.1 One of the most important factors affecting the efficiency of the flow of oil and gas mixtures is slippage, and in most of the experimental work that has been done no provision has been made for the measurement of this quantity. As Versluys pointed out, since there is no method now known to estimate it from the data usually taken; slippage must be determined empirically. This paper presents the results of some work carried on to, measure slippage in short experimental gas-lifts. As shown herein, slippage can be easily calculated in a vertical pipe carrying a mixture of oil and gas if the fractions of the pipe occupied by liquid and gas respectively are known. In this work, the fraction of the pipe occupied by the liquid was measured under a wide variety of conditions and the relationship between this fraction and other quantities, which are easily measured in ordinary work, was determined. It was hoped that the quantitative relationship obtained from this work could be used-for making accurate calculations in flowing or gas-lift wells, but unfortunately it did not check satisfactorily when applied to actual wells. Apparently flow in long flow pipes is mote efficient than in the short ones used for the experimental work. Nevertheless, it is felt that the data themselves are of interest; that the method of attack may be of value in future work and that the relationship derived between slip and the relative velocities is a contribution toward the solution of the gas-lift problem.

Jan 1, 1931

By Mario L. Villa

Another increase in production and the discovery of new pools arc the outstanding developments of the year 1937. Production in 1937 totaled 16,354,706 bbl., compared to 15,457,953 bbl. in the previous year, an increase of 5.8 per cent, of which 5 per cent was due to the Yacimientos Petroliferos Fiscales (Argentine Governnlent Oil Fields) and 0.8 per cent t,o private companies. Table I shows that the most important gain in output was obtained in zone B of Comodoro Rivadavia, partly offset by a 5.7 per cent decrease in the Neuqu6n district. The fields of Salta and Mendoza show an increase of 4.4 and 39.1 per cent, respectively. The determination of bottom-hole pressures was started by Yaci-mientos Petroliferos Fiscales (Y.Y.F.) in Comodoro Rivadavia and

Jan 1, 1938

By Karl J. Benecke

Though the first patent on a bucket wheel excavator (BWE) was granted in 1881 in the US, this technology was developed in Germany to the high standards of today. However, this development was only possible in parallel with development of shiftable belt conveyors and boom stackers. The combination of these three types of equipment in the open pits of the Federal Republic of Germany has made lignite the cheapest energy source for power generation, despite the low heating value of German lignite on the order of 8500 kJ/kg (3600 Btu/lb) only. Comparing the costs for fuels used in power generating on the basis of their heating value, the relation between lignite, high quality black coal, and imported crude oil is on the order of 1 to 1.5 to 2.5, hence highly in favour of lignite.

Jan 8, 1979

By Jim V. Rouse

In situ mining and dump leaching has been practiced for years. Recent environmental concern over conventional mining and milling techniques has rendered in situ mining more attractive. While there are many environmental advantages to in situ mining, there are disadvantages which, if ignored, can lead to environmental damages, followed by stringent control. The environmental advantages and disadvantages of the various types of in situ mining operations are discussed. Current legislation and regulations governing in situ mining are cited, together with a suggested program of environmental monitoring designed to protect the mining company as well as the environment. Suggestions are made for possible solution of existing pollution problems associated with previous mining activities by heap-leaching techniques. Present and indicated control of subsurface injection is traced, because of the many similarities in philosphy and monitoring requirements to in situ mining.

Jan 1, 1974

By R. E. Grim

With the exception of the extreme northeastern part of the state, Mississippi lies wholly within the Gulf Coastal Plains. The largest structural feature definitely proved is the so-called Jackson structure1 in the central part of the state. This structure is mainly the result of the burial of an igneous ridge on the old sea floor. The ridge trended in a northwest direction from about the town of Jackson in Hinds County into southeastern Arkansas. The present structure is the burial of the ridge. Recent detailed surface work by major oil companies has suggested smaller structures in other parts of the state, but so far they have not been definitely proved. Also considerable magnetometer and seismographic work has been done in the northern and central part of the state. The results of the operation of the seismograph are not yet available, but the magnetometer located many "magnetic highs" in this part of the state. Outside of the area of the Jackson structure, the exact cause for this magnetic variation is not known. In a portion of south Mississippi, considerable seismographic work has been done recently in an attempt to locate salt domes. While the details are not available, it has apparently met with little success. Prospecting by districts during the past year may be summarized as follows: Five wells of importance were drilled in the Amory district of east Mississippi. This district comprises all or parts of Monroe, Lee, Itawamba, Prentiss, .Alcorn and Tishomingo counties. Small gas was discovered at about 2500 feet. Several wells were drilled in the. Jackson district which is located in part or all of Hinds, Rankin, Madison and Yazoo counties. Some of these wells were abandoned and one was shut down most of the year

Jan 1, 1930

By J. W. Pugh, Sam Leber

Single crystals of tungsten were made and deformed in tension at 3000°C. The slip traces so formed on these crystals were analysed to determine the apparent slip system. Results indicate that deformation occurs in the<III> direction on planes of maximum shear stress. This determination agrees with the early work of Taylor and Elam on other body-centered cubic crystals at lout temperatures. SLIP in face-centered cubic and hexagonal close-packed metals has consistently manifested itself in straight traces which indicate that glide takes place on planes of highest atomic density and in directions of closest packing. The slip traces observed on body-centered cubic metals are, on the other hand, frequently branched and wavy, and indicate that while glide takes place in the direction of closest packing, it does not necessarily choose the plane of highest density. The early work of Taylor and Elam1 4 indicated that glide took place in the close-packed direction on planes close to those defined by the maximum shear stress. Subsequent investigations have tried to rationalize these observations in terms of an elementary process on the close-packed planes (110). For example, Elam5 and Grenin~er&apos; have suggested alternate glide on nonparallel (110) planes with the observed result that the summation of these glides results in a trace which defines some plane other than{110). Madden and chen7 have recently reviewed the phenomenological and theoretical aspects of noncrystallographic slip. More recently Koehler&apos; has presented a model of dislocation propagation which permits another rationalization. He indicated that dislocation loops are transferred from one glide plane to another by double cross-slip of screw segments. It is reasonable to assume that, on the average, such transfers may result in a trace which approaches the plane of maximum shear stress. The work described in this paper will show that

Jan 1, 1961

By John C. Calhoun, Frank T. Bethel

Glass beads have been surface treated with Dri-film to render them oil wet by n-octane to varying degrees, and capillary desaturation curves have been determined by the restored state method. The desaturation curves show a regularity of increasing displacement pressures as the oil wetness increases. This has been used to compute apparent contact angles between n-octane and water on glass. The family of desaturation curves also shows a regular crossover, such that the residual wetting liquid saturation values are in reverse order to the displacement pressures. A semi-logarithmic variation is shown between the apparent contact angle and the residual saturation. The desaturation data are interpreted to mean that the wetting liquid ceases to be a continuous phase within individual pores before the capillary pressure can be raised sufficiently to force out the wetting phase completely. The saturation of wetting liquid at which this break in liquid continuity occurs is higher as the oil wetness decreases. INTRODUCTION The petroleum industry has for some time been using measurements of capillary pressures on porous media for research correlations and engineering calculations. It has been generally recognized that the capillary desaturation curve reflects the character and arrangement of the pores within the media and the distribution of fluids within the pores. Methods have been proposed for computing pore size distributions, tortuosity factors. and relative permeabilities from capillary desaturation data.&apos; There is little doubt that the interactions between porous rocks and their contained fluids resulting from surface forces play a dominant role in determining the magnitude and direction of capillary pressure measurements. There have been attempts to introduce as variables two quantities — inter-facial tension and contact angle — generally used to char- acterize surface forces, but in spile of the wide interest in these quantities as important variables, few definite conclusions have been drawn concerning their qualitative or quantitative significance. INTERFACIAL TENSION The interfacial tension appears in a capillary pressure function given by Leverett for correlating capillary desaturation type curves. Use of the interfacial tension in this function seems to be justified by other experiments reported. Apparently, interfacial tensions have little bearing on wetting phase residual by desaturation. CONTACT ANGLE The contact angle was utilized as a variable by Bartell and co-workers"." in tests on displacement pressures, later recognized as the initial point of capillary desaturation. Although Leverett did not include contact angle in his original formulation of the capillary pressure function, later workers suggested its addition. Few reports are available to show variation of residual liquid with contact angle as a result of capillary desaturation.&apos; The problems attendant to measuring contact angle within a porous medium are great. As a consequence of the lack of a concrete approach to a measurement. the workers in this area of research have adopted the general expression of "wettability" to indicate the relative position of two liquids saturating a porous body. It has been shown that gross measurements on porous systems, including capillary desatura-tions, are sensitive to wettability. Attempts at giving a scale to wettability in terms of contact angle through capillary desaturation curves have been made and these apparently are steps in the right direction. In these attempts presence of many other variables precludes attainment of exactness. Also, as a result of other variables, it has been impossible to correlate changes in apparent contact angle with changes in other physical measurements of the systems in question. The present work is an attempt to eliminate as many variables as possible in measuring capillary desaturations resulting from changes in contact angle within a porous medium.

Jan 1, 1953

By George A. Miller

OIL, the abundance of it in the hands of the Allies and the lack of it in the hands of the Axis, played a major role in winning World War II. It bids fair to implement the winning of the peace. In fact the signing of the revised agreement on petroleum between the Government of the United Kingdom of Great Britain and Northern Ireland and the Government of the United States of America on Sept. 24, 1945, may be considered as the first step in establishing a new pattern in foreign relations by our Government. The significance of this agreement on petroleum is that it was arrived at on the part of the United States of America through the advice and consent of the most interested parties, the leaders of the petroleum industry and the Government, distinctly a first step toward unifying the power of business and the strength of the Government, which places us on a par with the British Crown which has always had the advice and counsel of its business leaders in formulating its foreign trade policies. And what is the thing so patently discernible in this new first step toward winning the peace? It is that the petroleum agreement, the first draft of which, signed in Washington on Aug. 8, 1944, almost caused an epidemic of apoplexy among the leaders of the oil industry, represents the desire of the people most concerned with the problems of petroleum both at home and abroad. This new agreement, which will come up before the Senate for ratification this month-hearings will commence in January - derives its "power from the consent of the governed," something about which our forefathers were vitally concerned once upon a time.

Jan 1, 1946

By Walter Kauenhowen

The production of crude oil in Germany during 1934 totaled about 2,200,408 bbl., a 33 per cent increase over the 1,670,109 bbl. produced in 1933. This is an extension of a yearly increase which has continued uninterruptedly since 1928. Producing Fields The 1934 increase in production is due chiefly to developments in the north district of the Nienhagen field, where the production in 1934

Jan 1, 1935

By B. C. Craft

Oil and gas development in Arkansas during the year 1933 has been marked by considerable wildcat drilling, considering the overproduction prevalent in the oil industry. Arkansas showed an increase in drilling operations during 1933. There were 45 completions from 10 counties resulting in 7 oil wells and 38 dry holes, compared with 37 completions resulting in 4 oil wells and 33 dry holes during 1932. Miller County continued to be the most active area, with 18 completions resulting in 3 oil wells and 15 dry holes. Extensive exploration around the Miller County field has more definitely established the producing limits. It has confirmed the belief that produc-

Jan 1, 1934

By William J. Millard

The Island of Trinidad has much the same geological history as the continent of South America. There are present in this area Cretaceous, Tertiary and Quaternary rocks, which were deposited in a basin covering eastern Venezuela and Trinidad, very much as rocks of the same age were deposited in the Maracaibo Basin in western Venezuela. Along the north coast there are metamorphosed and semimetamorphosed Cretaceous rocks which are found as semicrystalline limestone, schists and quartzites, etc. Both the Cretaceous and Tertiary rocks are petroliferous and are responsible for the production of oil in Trinidad and eastern Venezuela. The geological column in the oil-bearing region of Trinidad is shown below.

Jan 1, 1931

By David Reger

ONLY a few small pools of oil were found in West Virginia during 1924. The price of oil was so low that there was no incentive for active effort toward the discovery of new pools or the exploitation of reasonably certain productive areas. At present, several encouraging edge-pool developments are being held in reserve in the hope that a more favorable market is not far distant. In the old pools, wells are being carefully tended; there being little tendency toward abandonment. even in cases where production is temporarily unprofitable. In natural gas, however, the total value of which at the well mouth is now more than that of oil, the year has been busy and profitable. , The decline of old pools, together with the increasing demand, has caused the large operators who carry their gas to the consumer to make great efforts to preserve or increase the rate of production; while the small operators, who sell their product to the large companies at the well mouth, have been stimulated toward the same effort by more favorable prices. These conditions brought about the completion of a greater number .of gas wells in 1924 than in 1923. Few pools of gas have been discovered during the year, the principal production having been obtained in old areas and in the unusually large new territory that was revealed as potentially productive by the drilling of 1923. Some of these latter areas are still without pipelines but definite plans for getting most of this gas are now being executed.

Jan 3, 1925

By D. L. Pentz

The use of "probability" methods in slope stability analysis has been practised by geotechnical engineers for some time. This paper questions whether the term probability has been properly used since in many cases the term is used in a classical statistical manner only to describe frequency distributions of data. This paper proposes a definition of the term probability which includes the engineers&apos; subjective state of confidence for all critical parameters. Such parameters may include the slope stability model, undetected structural features, strength, groundwater pressure distribution, and geological framework. This process does not make a "better" analysis but it does force the geotechnical engineer to state his opinion in such a manner that others can understand and if necessary, criticize the assumptions. Further, this technique forces the question, "What impact would failure of a slope have on the production schedule or costs of a mine?" The level of risk taken in adopting a particular slope design strategy in a mine is not a question of what Factor of Safety should be selected but, rather, what trade-offs result from steeper slopes and the associated costs of failure. This paper also presents several simple probabilistic techniques which, though widely used in other fields have been all but ignored in geotechnical slope stability analyses. These include the use of stratified sampling to optimize Monte Carlo uncertainty approaches, and the use of simple functional approximations rather than complex stability models in probabilistic analysis. The author presents a case example of this technique and discusses the results in comparison with more traditional methods.

Jan 1, 1983

By M. P. Tixier, K. S. Kunz

A method for the interpretation of temperature curves recorded in gas producing wells is described. One essen-tial feature of the method is a simple graphical construction which conveniently reflects the amount of gas flowing from a given producing formation. This method, applied in conjunction with the Induction Log and radioactivity logs, is valuable to determine the points of entry of gas and to estimate the over-all thickness of the producing zones and their respective contributions to the total production. The method in particular is helpful in evaluating the effect of fracturing operations. An outstanding result of the application of the method is to bring to the light the relative importance of sand-shale interfaces in the production of gas. The paper is illustrated with field examp1es. INTRODUCTION The electrical logging tools involving conventional systems are not applied in wells which do not contain water base mud (empty holes, or wells filled with oil base mud), because of the absence of electrical connection between the electrodes and the surrounding formations. It is, therefore, common practice in this case to use other methods which do not require the presence of a conductive fluid in the borehole: resistivity log with scratcher electrodes, Induction Log, radioactivity logs, temperature log. . . . Such conditions are encountered in some regions, as the San Juan Basin, N. Mex., where a technique of drilling gas wells, using gas as a drilling fluid, has been introduced in the last two years. By the middle of 1953, an appropriate method for the logging of these wells was devised on the basis of field tests and of theoretical studies. It is the purpose of the present paper to give a description of this method. In these wells the logging operations are performed during the process of gas production, so that the temperatures in the boreholes are strongly affected by the cooling due to the expansion of the gas. On the other hand, a special thermometer, with a high sensivity and a short time constant, has been recently made available, which has enabled much more detailed and accurate recordings of the borehole temperatures than with the conventional instruments. As a result of these two circumstances, the temperature log constitutes the essential element of the method, in making possible the detection of the gas producing zones, the definition of their boundaries, and the estimation of the respective contributions of each separate zone to the total production. The method also involves the radioactivity and Induction Logs, as auxiliary documents. These logs in the present instance are helpful in the determination of the reservoirs. However, the information they give in this respect is limited. This comes from the fact that, due to the absence of the MicroLog and/or MicroLaterolog and of the SP log, the estimation of formation factors and connate water salinities is somewhat conjectural. Furthermore, little help is obtained from the Neutron log for the evaluation of porosity and of formation factor because the variations of gas saturation affect the Neutron log in a way similar to the variations of porosity. It should be said also that even an exact knowledge of the gas saturation of the reservoir beds would not

Jan 1, 1956

By F. Weinberg, L. MacAulay

DAVIS,&apos; in an investigation of solute redistribution along molten rods of dilute silver in tin, concluded that at horizontal temperature gradients below approximately 5°C per cm very little convective mixing takes place. Cole and winegard2 observed temperature oscillations in horizontal melts of tin, with temperature gradients of several deg per cm. They associated the temperature oscillations with the presence of convective flow in the melt. At temperature gradients less than 1°C per cm they did not detect convective flow. In the present work, direct measurements of con-vective flow in liquid tin have been made using a radioactive tracer technique. The results indicate that extensive convective flow occurs at temperature gradients below those previously reported. The apparatus used to determine the extent of con-vective flow is shown in Fig. 1. The graphite boat Fig. l(a), has two rectangular channels both of which contain molten tin. Radioactive Ag110 in the form of Sn-0.2 pct Ag alloy was introduced at the end of one channel, by rotating the cylinder shown. A series of fixed thermocouples were positioned along the center of the second channel to determine the temperature gradient. It was assumed that the two channels had identical temperature distributions. The graphite boat was inserted into a vycor tube which was surrounded by a multiple winding tube furnace as shown in Fig. l(b). The tin was melted in an argon atmosphere. The distribution of Ag110, as a function of position along the boat at a given time after introduction of the ~g"&apos;, was determined with the

Jan 1, 1970

By Forrest V. Williams

The dislocatiorl and stacking-fault structuve of epitaxial GaAs1-,PX lms been examined by chemical etching. The layers were groun in the (100) direction and etch Pils were developed on (111} planes which nad been lapped and polished on the epiLaxia1 layevs. Tile effecL of the jollolcing cariables on the quality of the epilaxial layers has been examined: doping leuel, grouth rate, and composition. High stacking-faullL densilies weve found in the GuAsi_xpx layers. These are not observed in heavily dolled epitaxial layers tzar in layers with low phosphorus compositions. The dislocatiorz density in GuAsi-x px was highest at the sub-stvate- epilaxia1 layer interface. Composilion changes introduced dislocations in the epitaxial layers. ManY semiconductor p-n junction lasers of Group TIT-Group V compounds and their alloys have been reported in the past several years. Laser action at visible wavelengths in GaAsl-x,Px was first reported by Holonyak and Bevacqua. GaAs, a direct transition semiconductor which lases, and Gap, an indirect transition semiconductor which does not lase, form a continuous series of solid solutions.2 Laser junctions can be fabricated in GaAsl-xPx crystals with phosphorus compositions up to about 40 mol pct. In addition to the production of coherent radiation in these crystals, the efficient recombination radiation of p-n junctions in this material has equally important potential in the development of low-power semiconductor lamps. To achieve a high conversion efficiency of electrical to optical energy in p-n junctions in this material, the relation of physical properties of the crystal to luminescence efficiency must be better understood. Although the electrical, optical, and device properties of GaAsl -xPx junction lasers are understandably of considerable interest, the work to date indicates that the more serious problems are the chemical and metallurgical difficulties encountered in the growth of this material.3 In addition to the problems of chemical purity, crystal imperfections, such as dislocations and stacking faults, can be expected to affect both the efficiency of the radiative recombination process and the perfection of the p-n junction.3 The last requirement, i.c., that of the perfection of the p-n junction, is a particularly troublesome one in the fabrication of laser diodes. To obtain good laser diodes, the p-n junction must be flat, which permits the radiation to be reflected from the resonant cavity boundaries. Junction planarity is extremely sensitive to the crystal perfection of the semiconductor material. Also, it is known that at high dislocation densities (-105 per sq cm) it has not been possible to build laser junctions in GaAsl-xPx . Few studies have been reported on the crystal defect structure of GaAsl-,P,. The first serious study seems to be that of Wolfe, Nuese, and Holonyak,3 who examined the dislocation structure of monocrystalline bulk (nonepitaxial) material grown by halogen vapor transport. In this paper are reported some observations on the dislocation and stacking-fault structure of GaAsl_,P, crystals grown by a vapor transport process on substrates of GaAs. EXPERIMENTAL Crystal Growth. The GaAsl-xPx crystals were grown in an open-tube flow system, using two sets of reagents. GaAs, Pr(red), and HC1 were employed in one method. The transport reaction is =950JC GaAs+HC1 = GaCl +1/4As4 +1/2H2 and the deposition reaction is 2GaAs1-xPx +GaCl3 Composition control is obtained by the flow rate of the HC1 and the vapor pressure of the P4, which is maintained in a separately controlled furnace. The second method has been described by Ruehr-wein4 and utilizes gallium, AsH3, PH3, and HC1. The same transport and deposition reactions as above are involved. Composition control is obtained solely by the flow rates of the three gases involved. All of the crystals were grown on chemically polished GaAs substrates oriented on the (100) plane. The thicknesses of the epitaxial layers were typically 100 to 300p. Revealing of Dislocations. Dislocations were re-vealed on both the( 111 ) and { l l l }b faces by chemical etching. The specimen to be examined was mounted at 54.7 deg, lapped on glass with 3-p alumina, polished on cloth with 3-p diamond paste, and, to remove work damage, chemically polished at room temperature for

Jan 1, 1968

By J. H. Bramwell

THE following experience in rebuilding a furnace crucible while in blast may not be wholly uninteresting to some, notwithstanding its purely practical character. Few are aware of the frequent calls made on a furnace manager&apos;s skill and ingenuity, to meet the irregularities which present themselves with kaleidoscopic variations in the operations of furnaces. Unfortunately the methods pursued in overcoming these practical difficulties are too seldom recorded, and much valuable information is lost that could not fail to be of value to many, and to none more so than the educated technical manager, with a limited practical experience, who, without a literature or record of any kind to refer to, finds himself, in times of emergency, dependent and looking for assistance from those whom it is his province to instruct and direct. With positive data, however, that like difficulties have been successfully overcome, he can confidently resort to similar expedients, with such modifications as the circumstances may demand in his particular case, and pull through seeming impossibilities in the face of ignorant prejudice. The Quinnimont Furnace (60 x 15 feet) had been in operation but two months, when it became necessary to draw the tuyeres out a distance of 18 inches, in order to give them a resting-place; the brickwork under them being completely cut away, so that after each

Jan 1, 1877

By Howard L. Hartman, Eugene P. Pfleider

The paper relates to the laboratory and pilot plant studies that have been carried out by Sherritt Gordon Mines Ltd., Metallurgical Research Div., in developing the ammonia pressure leach process for extracting Cu, Ni, Co, and S from high grade Ni concentrate produced from Lynn Lake ores and describes in some detail the chemistry of the process. In the leaching stage air, ammonia, and sulphide minerals react in a sequence of inter-related steps to produce soluble amines of Ni, Cu, and Co in a solution containing sulphate, thiosulphate, polythionate, and sulphamate ions and a controlled amount of free ammonia, the iron and other components of the concentrate remaining as an insoluble residue which is separated from the leach solution by filtration. The pregnant solution produced in leaching is further treated by boiling to precipitate and remove Cu as cuprous sulphide, leaving a copper-free solution with a composition suitable fir subsequent precipitation of Ni and Cu by H,. The progress of individual reactions in leaching and copper removal is discussed. The effect of variables such as temperature, pressure, ammonia concentration, particle size, and agitation is outlined and the technique of thionate control in leach solutions is described. Data is given for the physical and chemical reactions involved in precipitating copper from leach solutions as Cu sulphide by boiling.

Jan 1, 1956

By P. Somasundaran, K. P. Ananthapadmanabhan

A knowledge of the role of effects and interactions of chemical species is important in developing an understanding of the behavior of mixed minerals and natural ores in beneficiation processes such as flotation and flocculation. In this study the role of such species was examined for the calcite-apatite system by conducting flotation of each mineral in various supernatants prepared by mixing with water. Supernatants of apatite and even that of calcite depressed the flotation of calcite markedly in the pH range of 5 to 13. Addition of Ca(NO3)2, K2C03, and K3P04 also produced definite effects under various pH conditions. Apatite flotation was also affected by the mineral supernatants and by carbonate and phosphate solutions. The results are analyzed in terms of the surfactant&apos;s solubility properties and the mineral&apos;s electrochemical and dissolution properties. While depression of calcite flotation by the dissolved species is found to be governed by depletion of oleate by bulk precipitation, the depression of apatite flotation is caused by the carbonate and phosphate species in the system. Turbidity measurements and a thermodynamic analysis of possible interactions in the system support these considerations. The effect of the supernatant of minerals on their own flotation suggests the important role of kinetics of various surface interactions in comparison to that of mineral dissolution.

Jan 1, 1985

By Y. C. Liu, G. A. Alers

Using X-ray pole-figure information and the single-crystal elastic constants, the angular variation of an elastic modulus in a polycrystal can be calculated and compared to measured clalues. This procedure has been used in the past to provide supporting ecidence for a particular choice of ideal orientations in the description o the X-ray pole figure. Since it is well-known that the absolute value oj an elastic modlus oj a poly crystal cannot be acczrralely calculated from the single-crystal elastic constants, there exists a serious question about the reliability oj this modulus method in the study of textures. This paper deriz-es sez3eral simple fornzulae for the ntzgular lariatiion of Young&apos;s modulus in the plane o a rolled sheet sing the same ssuinptions which lead to the lack oj detinztion of the absolute c&apos;alre OJ the elastic ,nodulus. The vesults show that, although the absolute isallre oj Young&apos;s modulus depends strongly on the assumptions made, the shape of the modulus vs angle curve is not very sensitive to the assumptions and thus can be used reliably in texture studies. Exatzples oj&apos; using this criteriotz are illustrated in the text. NeARLY all poly crystalline materials have some preferred orientation in the arrangement of their grains and hence exhibit anisotropy in their properties. This preferred orientation is usually measured and studied by X-rays which yield detailed information on the statistical distribution of grain orientations in the form of pole figures. The usefulness of these pole figures in theories of texture formation and in predictions of properties has come to depend almost entirely on the characterization of the pole figure by one or more ideal orientations. Unfortunately, this characterization is not unique and different authors often present different ideal orientations to characterize a given pole figure. In order to distinguish between these different choices of ideal orientations, it is necessary to go beyond X-rays and consider other physical properties which reflect the texture&apos; simply because any choice of ideal orientations must predict correctly the observed anisotropy in all physical properties. The most common example of this procedure has made use of the angular variation of Young&apos;s modulus with respect to the rolling direction in the plane of a rolled sheet.3 4 Here the anisotropy can be measured easily and it can also be calculated from the single-crystal elastic constants and the chosen ideal orientation. Unfortunately the methods used to calculate this anisotropy were chosen for their simplicity rather than for their mathematical rigor so that there exists a serious question as to the validity of conclusions reached by this modulus method. It is well-known5 that the absolute value of the Young&apos;s modulus of a polycrystalline aggregate cannot be calculated very accurately because different mathematical averages over the grains yield different results. It is one purpose of this paper to examine the effect of different averaging procedures on the calculated anisotropy of Young&apos;s modulus in the rolling plane of rolled sheets in order to see if this property can be used reliably in texture studies. This particular modulus and type of material were chosen because the modulus is easily measured and rolled sheet is technologically important. The results show that, although different averages yield different absolute values for Young&apos;s modulus, the shape of the modulus vs angle curve is not very sensitive to the averaging procedure and thus can be used as a criterion to check the various ideal orientations used to characterize the X-ray pole figure. Examples of this checking procedure are given in the final section. Another purpose of this paper is to examine the possibility of using the anisotropy of Young&apos;s modulus as an indicator of texture without reference to pole figures or ideal orientations. Such a use would require that different textures yield quite different shapes for the modulus vs angle curve so that the distinction between textures would be quite clear. The experimental results presented in the final section indicate that there is easily enough variation in shapes to allow modulus measurements to be useful texture indicators, par-

Jan 1, 1967