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By F. J. Fayers, R. L. Perrine

For many years the problem of increasing ultimate recovery of oil from a reservoir has been a subject of interest to the oil industry. At present, a standard secondary recovery technique is to flood the reservoir with water once natural forces of the system are depleted. The permeability characteristics of the rock, together with interfacial forces which exist between the two fluids and the porous material. allow only part of the oil in the rock formation to be recovered by the water-flooding process. Laboratory experiments have shown that when detergents are added to the flooding water, the flow properties of oil in a porous rock arc improved. This improvement results in greater oil recovery. Even though higher recoveries are obtained using detergents, the extra cost associated with the method may make it economically unsatisfactory. To establish economic feasibility requires experimental laboratory measurement of fluid and rock properties together with a calculational procedure to predict field results. Pilot tests in the field may also be required. This paper presents a mathematical procedure for predicting detergent flood behavior. A number of reasonable simplifying assumptions are made to obtain a tractable system of equations. The resulting method may be regarded as a generalization of Buckley-Lev-crett' theory to solve simultaneously for water saturation and detergent concentration profiles. Consequently this type of calculation can be used in much the same manner as Buckley-Leverett theory is used to evaluate a water flood. The mathematical method employed is the so-called method of characteristics for solving hyperbolic partial differential equations. This application of the method is instructive because several other problems in reservoir analysis may be analyzed in a similar manner. FLUID FLOW EQUATIONS The flow behavior of oil and water without detergent through porous reservoir rock is usually expressed by Darcy's law and a continuity equation for each phase. If gravitational forces are neglected, vrg = kr (s)µr v p rg.........(1) vrg = kr (s)µr v p rg.........(1) ? pa va = F ?/?t (sd) where v is the volumetric flux, k represents permeability, S is saturation, and P the pressure. Fluid viscosity is denoted by 11, p is the density, 4 is porosity, and I the time. The subscripts w and o refer to water and oil. The capillary forces in the system lead to a difference in pressure between phases. This may be expressed by the relation: Pm -P0 =Pc(S).........(5) The capillary pressure? P,, is determined experimentally as a function of saturation. DETERGENT BALANCE EQUATION Addition of detergent to the water phase affects the flow properties of the system. Capillary pressure and relative permeability become functions of detergent concentration, c, as well as fluid saturation. That is: P--P (S,c) and k,,,.- - -- k,,,. At low oil saturation values, the presence of detergent reduces capillary pressure and reduces the relative permeability ratio. Detergents are surface-active and adsorb on rock surfaces. The quantity adsorbed, a, will depend on the concentration c of detergent solution and may also depend on the saturation; thus, a = a(S,c). In this analysis we have assumed that the detergents used are water soluble but not oil soluble, and their movement is therefore restricted to the water phase. The dispersion of detergent in water is neglected by comparison with transfer by flow within the system. Detergent movement is determined by the water flux and adsorption: ? cv m = -F ?/?t (cs + a) We will assume that the quantity of detergent in solution is too small to significantly change water density or viscosity. When the permeability and capillary pres-

By K. C. Gilbart, Edgar Stansfield

One of the most striking features of the coal series passing from peat through brown coal, lignite, etc., up to anthracite is the gradual reduction of moisture content with the increased coalification of the original plant material. Thus drained peat from a bog may contain 90 per cent water, brown coal contain 50 per cent, lignite 30 per cent, while a bituminous coal may contain only 1 per cent moisture. Moisture, therefore, is one of the important factors to be considered in coal classification, especially with the lower rank coals. With bituminous and higher rank coals the moisture content is less satisfactory for classification; it may even pass a minimum value and then increase with increasing rank to anthracite and superanthracite. Coal in an undisturbed seam contains moisture which is an integral part of the coal, but it may also be wet with free, underground water percolating through the seam. Only the former must be considered in evaluating the moisture content of the coal for classification purposes; this will be called the "true moisture" of the coal. When the seam is mined and sampled the sample taken may show the true moisture; on the contrary, it may contain in addition free mine water or, especially in dry, well ventilated mines, it may contain less than the true moisture. Coal contains unstable organic compounds which may decompose, with the production of moisture, when the coal is exposed to air at ordinary temperatures, or is heated with or without exposure to air. The potential moisture of a coal therefore is higher than its actual moisture. The lower the rank of the coal, the greater its instability, as a rule, and the greater the care necessary to avoid oxidation or decomposition in any investigation of moisture content. The majority of coal workers have preferred, on account of the difficulty in evaluating the true moisture of a coal, and for other reasons, to classify coals by analyses calculated to the dry-coal basis. A number of workers familiar with lower rank coals have recently insisted that the classification of such coals can be satisfactory only if analyses on the moist-coal basis are employed. The moisture-holding capacity of coal is therefore intimately connected with coal classification, and in this paper a procedure is outlined for determining the true moisture of a coal,

Jan 1, 1932

By Clarence Thom

This chapter presents, in summarized form, standard procedures for making separations of minerals from their ores by the froth flotation process to produce marketable concentrates. These are typical mineral separations which are being made commercially with the reagents and conditions generally used in the mining industry. Typical separations are presented for 17 metallic and 11 nonmetallic ores. The review of each includes a brief description of the mineral and the particular problem presented, general market specifications for its concentrates, an outline of treatment method, and kinds and quantities of reagents usually employed. This chapter does not include de- tails about ore preparation (crushing, grinding, and classification), elements of ore and pulp transportation (conveying and pumping), or concentrate preparation for market (thickening, filtering, and drying). In each presentation it is assumed, if not detailed further, that the ore is ground to the economical point of liberation of the minerals to be separated. Specific information, such as ratio of concentration and recovery, that depends upon the grade of ore being treated is considered beyond the scope of this chapter. Effective flotation separations that produce marketable concentrates may produce widely varying results in terms of percent recovery and still be economically profitable operations. Details of plant practice on specific ores are presented in Chapters 16 and 17. In this chapter the chemical names of the reagents are given. The extent to which different reagents are used in flotation plants in the U. S. is presented in Chapter 4. A compilation of the various flotation reagents, their trade names, manufacturers, and use has been prepared by H. T. Spedden. ANTIMONY The principal ore mineral of antimony, stibnite (Sb2 S3), is generally found in the U. S. in ore bodies in association with other valuable minerals such as galena (Pbs), sphalerite (ZnS), chalcopyrite (CuFeS2), or tetrahedrite (3Cu2 S – Sb2 S3), The sulfo-salt minerals of antimony, such as tetrahedrite or pyrargyrite, are often associated with high silver values, so that the presence of antimony may indicate economic importance even though the actual antimony content is low. Antimony is also significant to the mineral economy because of its occurrence in some ores where lead, gold, and silver are the

Jan 1, 1962

By B. Das, V. Hucka

In light of the present energy crisis, coal appears now as the only reliable source of energy. The production of coal is expected to regain a rising trend after the latest slump. Aside from the competitive price with natural gas and oil, the other retarder of coal production is its environmental pollution effect. Gasification of coal has been advanced as the partial solution to the energy-ecology crisis. All the Advantages In situ gasification of coal may be considered a further step in this direction. It carries all the advantages of normal coal gasification as a stable source of energy; it is clean to handle and nonpolluting of the environment. It partially and sometimes fully does away with mining, makes uneconomical low grade coal and lignites economical and places some formerly unworkable seams within the scope of modern technology. The seams posing problems for mining due to tectonic disturbances may be converted into gas in situ. Low grade coals, such as lignites, which otherwise would be left in nature as uneconomic wealth, may be exploited by underground or in situ gasification. Thus, in situ gasification is likely to increase the exploitable reserves of coal and may reduce the cost of production. An additional merit of this method is that coal substance never reaches the surface and there is no problem of cinder disposal.

Jan 8, 1973

By Jackson M. Langton

Substantial evidence supports the theory that high-angle faults and overthrusts in the Morenci-Metcalf region were initially caused by a Late Precambrian-Early Paleozoic stress field. These faults were reactivated in Late Paleozoic-Early Mesozoic time which completed the structural framework prior to the Laramide Orogeny. Excluding an interruption by diabase dikes and sills, Paleocene-Eocene magmas invaded the pre-existing structures and became progressively more sialic in composition and nearer to the surface with each subsequent injection. The last sialic intrusion was highly explosive, rendering the country rocks more permeable for hypogene and supergene activity. Widespread dilation, instigated by uplift and subsequent magma intrusion, caused extension to the northwest and southeast. A major locus of hypo gene alteration and mineralization appears to be centered around the south and southeast periphery of the youngest granite porphyry stock. A potassic, sulfide-deficient core is telescoped by a pyritic, phyllic zone which in turn is enveloped by widespread propylitic alteration.

Jan 1, 1974

Separates of all the Technical Publications published in 1931 are available at Institute headquarters. All the papers are on file in public, university and technical libraries, and when so indicated in the list, may be found in the Transactions. Copies of these papers have been mailed to those members of the Institute who are registered in the different classes: A-Metal Mining; B-Milling and Concentration; C-Iron and Steel Division; D-Nonferrous Metallurgy; E-Institute of Metals Division; F-Coal Division; G-Petroleum Division; H-Nonmetallic Minerals; I-Mining Geology; K-Mining Administration; L-Geophysical Prospecting. Other members may obtain copies by writing to the Secretary. Additional copies are sold at the rate of I cent per page; minimum charge, 25 cents. Metal Mining Tech-nical Publi- Title Author Meeting TRanb. cation Volume No. and Page* 411-A.43 Ventilation at the Portovelo Mines, J. P. Harmon New York. T31, 83 Ecuador (18) Feb., 1931 425-A.44 Use of Models for the Study of Mining P. B. Bucky New York, Problems (28) Feb., 1931 Milling and Concentration 375-B.32 Ball Mill Studies, I (53) A. W. Fahrenwald New York, H. E. Lee Feb.. 1931 401-B.33 Experimental Flotation of Oxidized H. S. Gieser New York. Silver Ores (9) Feb., 1931 410-B.34 Flotation of Minor Gold in Large-scale E. S. Leaver New York, Copper Concentrators (32) J. A. Woolf Feb., 1931 414-B.35 Effect of Particle Size on Flotation A. M. Gaudin New York, (23) J. 0. Groh Feb., 1931 H. B. Henderson 416-B.36 Ball Mill Studies, 11.—Thermal A. W. Fahrenwald New York. Determinations of Ball Mill Effi- G. W. Hammar Feb., 1931 ciency (13) H. E. Lee W. W. Staley Iron and Steel Division 38QC.59 Open-hearth Steel Process as a Prob- E. R. Jette New York, C31, 80, 111 Iem in Chemical Kinetics (34) Feb., 1931 381-C.60 Thermodynamic Study of the Phasial Yap, Chu-Phay New York. Equi1ibriain the System Iron-car- Feb., 1931 bon (26) 382-(3.61 Influence of Dissolved Carbide on the Yap, Chu-Phay New York, Equilibria of the System Iron-car- Feb., 1931 ban (19) 383-C.62 Research on Blast-furnace Slags. R. S. McCaffery New York, Three papers (88) Co-workers Feb., 1931 384-C.63 Statistical Analysis of Blast-furnace K. S. McCaffery New York, C31, 60, 70 Data (13) R. G. Stephenson Feb., 1931

Jan 1, 1931

By Eugene Leonardon

THE search for oil has required, and without a doubt supplies, a tremendous amount of information on the structure, composition, physical properties, and history of sedimentary rocks. The earliest and most complete source of knowledge is the sample or core of the rock itself, the uses of which are well known. The purpose of this paper is primarily to discuss a new method for obtaining these cores, and to illustrate its use in connection with electrical logs. Most cores have been obtained through a special adaptation of rotary drilling, and the results have been remarkably good, considering the mechanical problems involved. Unfortunately, because of the time and expense, this method cannot be used for the entire length of the drill hole. Even though ingenious contrivances have been evolved in order to reduce the time spent in round trips, such as wire-line coring equipment, mechanical coring still remains too expensive to be carried out con-tinuously. In practice, therefore, one is finally compelled to estimate the probable depths of the more interesting horizons and, allowing a wide margin of safety, to core through those sections only. It is true also that interesting results have been obtained by examining the cuttings brought to the surface by the mud circulated in the well during the process of drilling. Be that as it may, the inescapable fact remains that key horizons may be passed inadvertently, for one reason or another, while the drilling operations are being performed. The only continuous record of the formations encountered is that furnished by electrical surveys. Obviously, it would be desirable to make the electrical survey first and to take the samples from the wall of the hole according to the indications on the electrical log. In this way, it would be possible to core only the exact sections desired, eliminating the otherwise inevitable estimates as to the point at which to start coring, and thereby reducing to a minimum this expensive operation. At the same time this method would provide a maximum' of useful samples.

Jan 1, 1939

By Eugene Leonardon

THE search for oil has required, and without a doubt supplies, a tremendous amount of information on the structure, composition, physical properties, and history of sedimentary rocks. The earliest and most complete source of knowledge is the sample or core of the rock itself, the uses of which are well known. The purpose of this paper is primarily to discuss a new method for obtaining these cores, and to illustrate its use in connection with electrical logs. Most cores have been obtained through a special adaptation of rotary drilling, and the results have been remarkably good, considering the mechanical problems involved. Unfortunately, because of the time and expense, this method cannot be used for the entire length of the drill hole. Even though ingenious contrivances have been evolved in order to reduce the time spent in round trips, such as wire-line coring equipment, mechanical coring still remains too expensive to be carried out con-tinuously. In practice, therefore, one is finally compelled to estimate the probable depths of the more interesting horizons and, allowing a wide margin of safety, to core through those sections only. It is true also that interesting results have been obtained by examining the cuttings brought to the surface by the mud circulated in the well during the process of drilling. Be that as it may, the inescapable fact remains that key horizons may be passed inadvertently, for one reason or another, while the drilling operations are being performed. The only continuous record of the formations encountered is that furnished by electrical surveys. Obviously, it would be desirable to make the electrical survey first and to take the samples from the wall of the hole according to the indications on the electrical log. In this way, it would be possible to core only the exact sections desired, eliminating the otherwise inevitable estimates as to the point at which to start coring, and thereby reducing to a minimum this expensive operation. At the same time this method would provide a maximum' of useful samples.

Jan 1, 1939

By Nicholas J. Grant, Ernest P. Abrahamson

IN recent work, Bloom and Grant' and Stein and IGrant' have indicated that a high temperature chromium phase exists. In the 68 pct Cr-Ni binary they found a eutectoid reaction, P chromium transforming to a chromium plus y nickel at 1215°C. Un-

Jan 1, 1957

By R. L. Stone

None of the currently used methods of testing bentonites as binders for strengthening iron ore pellets is entirely adequate by itself. Since more knowledge was needed about 1) which properties of bentonite most affect pellet strength, and 2) the precise mechanism by which strengthening is produced, attention was paid to possible new techniques for rating bentonites. With the structural nature of bentonites — in particular, the montmorillonite component — the possibility of rating bentonites on the basis of zeta potential was investigated. These bentonites were also rated by conventional tests and measurements, including colloid content, barrel yield, pH, chemical analysis and physical tests on green and dry pellets. A mechanism for pellet bonding based on electro-kinetic forces between the bentonite and the iron ore concentrate appears to be feasible. In pelletizing, from 6 to 18 lbs of bentonite is added per ton of concentrate to give strength to the green and dry pellets. In some operations even more bentonite than is required for strengthening purposes must be added for moisture adsorption to pennit balling of the concentrate. Since bentonite is thus a major item in pelletizing, more knowledge about the way in which bentonites act as binders and better ways of rating this ability would help in the difficult job of selecting the right bentonite for a given concentrate. The fact of the matter is that although several methods are in current use for testing bentonites, none of these methods are consistently foolproof. For example, a given bentonite may rate high by several standard tests yet turn out to be a poor binder, and of course the reverse also occurs. Actually, more knowledge is needed about 1) which properties of bentonite most affect pellet strength, and 2) the precise mechanism by which strengthening is produced. In this study attention is therefore paid to possible new techniques for rating bentonites. With the structural nature of bentonites as a starting point, we investigated the possibility of rating bentonites on the basis of the zeta potential, i.e., the electrokinetic ootential on the montmorillonite colloids — the main component of bentonite binders. The zeta potential technique was applied to a range of commercial bentonites from several areas in the U.S. and abroad. These bentonites were also rated by conventional tests and measurements, including:

Jan 1, 1968

By Morris Cohen

WITHIN the past two years, a number of publications have called attention to the double peaks, or stages, that appear in the hardness and strength curves of certain aging alloys. The author has shown the existence of double hardness peaks during the aging of a high-purity silver-copper alloy;1 and on the basis of electrical resistance, microscopic, dilation and lattice-parameter measurements, he concluded that the initial hardness peak occurs prior to precipitation while the secondary hardening is due to precipitation. It was suggested that the general mechanism of age-hardening involves two consecutive processes, the first consisting of nucleus or knot2 formation, and the second consisting of actual precipitation and particle growth. It was further held that the two stages are interdependent, but because of nonuniform precipitation they may overlap each other to an extent that increases as the aging temperature is raised. At high aging temperatures, the effect of the first stage cannot be detected because of the rapid occurrence of precipitation. The general theory of age-hardening recently presented by Dr. M. L. V. Gayler3 is in close agreement with the picture outlined above. With reference to work done on duralumin, copper-beryllium and copper-silver alloys, Dr. Gayler also concluded that age-hardening takes place in two consecutive steps: first, diffusion (in which the solute atoms migrate to certain crystallographic planes), and then precipitation. However, W. L. Fink and D. W. Smith4 have shown that the double aging peaks that appear in the strength curves of high-purity aluminum-copper alloys may be explained without recourse to pre-precipitation phenomena. By means of very careful metallographic technique, Fink and Smith demonstrated that during aging the precipitation takes place at an accelerated rate along the grain boundaries and slip planes as a result of the plastic deformation caused by the drastic quench from the solution heat-treatment temperature. ? The general precipitation occurs at a

Jan 1, 1938

By Morris Cohen

WITHIN the past two years, a number of publications have called attention to the double peaks, or stages, that appear in the hardness and strength curves of certain aging alloys. The author has shown the existence of double hardness peaks during the aging of a high-purity silver-copper alloy;' and on the basis of electrical resistance, microscopic, dilation and lattice-parameter measurements, he concluded that the initial hardness peak occurs prior to precipitation while the secondary hardening is due to precipitation. It was suggested that the general mechanism of age-hardening involves two consecutive processes, the first consisting of nucleus or knot' formation, and the second consisting of actual precipitation and particle growth. It was further held that the two stages are interdependent, but because of nonuniform precipitation they may overlap each other to an extent that increases as the aging temperature is raised. At high aging temperatures, the effect of the first stage cannot be detected because of the rapid occurrence of precipitation. . The general theory of age-hardening recently presented by Dr. M. L. V. Gayler3 is in close agreement with the picture outlined above. With reference to work done on duralumin, copper-beryllium and copper-silver alloys, Dr. Gayler also concluded that age-hardening takes place in two consecutive steps: first, diffusion (in which the solute atoms migrate to certain crystallographic planes), and then precipitation. However, W. L. Fink and D. W. Smith4 have shown that the double aging peaks that appear in the strength curves of high-purity aluminum-copper alloys may be explained without recourse to pre-precipitation phenomena. By means of very careful metallographic technique, Fink and Smith demonstrated that during aging the precipitation takes place at an accelerated rate along the grain boundaries and slip planes as a result of the plastic deformation caused by the drastic quench from the solution heat-treatment temperature. † The general precipitation occurs at a

Jan 1, 1938

By W. I. Duvall

A brief review of the resonant frequency and ultrasonic pulse methods for obtaining elastic constants of rock samples shows that the equations for an iso-tropic elastic solid commonly used to calculate Young's modulus, modulus of rigidity and Poisson's ratio can result in appreciable error if the rock is even slightly anisotropic. Consideration of the equations that relate bar velocities and free medium velocities to elastic constants for orthotropic, transversely isotropic and isotropic solids shows that a combination of the two methods can be used to determine average elastic constants for a single sample of rock. The determination of elastic constants in different directions requires a large number of tests on oriented samples. The use of both the resonant frequency and ultrasonic pulse methods is recommended so that the determination of both Young's modulus and modulus of rigidity is independent of the determination of Poisson's ratio. The dynamic elastic constants of rock can be determined in the laboratory from measurements on small samples which may be in the form of right circular cylinders (diamond drill core). Either the resonant frequency6 or ultrasonic pulse method1 can be used to determine the longitudinal and shear velocities in the same specimen. The resonant frequency method provides a measure of the longitudinal bar velocity, V,, and the torsional bar velocity Vt; whereas the ultrasonic pulse method provides a measure of the free medium longitudinal velocity, Vp, and the free medium shear velocity, V, . The elastic constants (Young's modulus E, modulus of rigidity G, and Poisson's ratio v) are calculated from the density of the specimen, p, and one of the pairs of velocities by means of equations from isotropic elastic theory. For the resonant frequency method the equations are: It should be noted that Eq. 5 is derived from Eq. 4 and 6 and the relation between the elastic constants for an isotropic solid as given by the first part of Eq. 3. The in situ determination of dynamic elastic constants is accomplished by generating a complex seismic pulse in the rock and measuring the arrival times for the longitudinal and shear phases of the pulse at two distant points.5 From these travel times and the distance of the travel path both Vp and Vs are determined. The density of the rock is determined from samples in the laboratory, and Eq. 4 to 6 are used to calculate the elastic constants. These three methods involve the assumption of isotropy and perfect elasticity, and require the use of the relation v = (E/2G) - 1, which holds only if the elastic constants are the same in at least two directions. The calculation of v by means of Eq. 3 introduces considerable error, as a 1% error in V, and V, results in a 20% error in v. If frequencies for samples with a length-to-diameter ratio greater than four and a length greater than 8 in. are measured carefully, the experimental error can be kept to 1%. However, it is not unreasonable to expect that the variation in Vb and Vt with direction may exceed 1%. Thus, for even a small percentage of anisotropy the use of Eq. 3 can result in considerable error in v. The calculation of v by Eq. 5 also involves some uncertainty as a 1% error in Vs and Vp can result in a 6% error in v. By means of the pulse method both

Jan 1, 1965

By H. W. Gudenau, R. S. Chatty, W. Wenzel, M. Ponthenkandath

During several experimental programs conducted at the Institute of Ferrous Metallurgy, Technical University, Aachen, whisker formation was observed when iron ores were reduced at low as well as at high temperatures. Thus, in an attempt to find the reason for the volume change taking place during reduction, iron whisker growth was observed. Whisker growth appears to be one of the important reasons for the swelling of pellets. One set of experimental observations determined that when iron forms as needles rather than as a crust on the surface of oxide, the pellets became very porous. In related experiments, the beneficiation of finely disseminated iron ores, in which the metallic iron is separated from the gangue in granular or nodular form, was achieved by a reduction-concentration method. In this process, which is conducted at sufficiently high temperatures, oxide whisker growth, resulting from the formation of volatile suboxides and a gas transport mechanism, plays a vital role in the joint deposition of SiO, and iron from the vapor stage.

Jan 1, 1973

By C. W. Phillips, R. S. Busk

With most cast metals the grain size may vary within wide limits, depending upon the conditions at the moment of freezing. These conditions are subject to control in magnesium-base alloys, by proper melting and superheating techniques, enabling production of quite uniform and fine-grained castings, almost independent of section thickness. However, such variations of grain size as do exist, in common with all metals, are reflected in corresponding changes in mechanical properties. It is the intent of this paper to present data giving the relationship between grain size and mechanical properties. Data are also included on the combined effects of grain size and micro-porosity. In addition, a short discussion of factors influencing the grain size of sand castings is included. Measurement OF Grain Size By grain size is meant the statistical distribution of volumes occupied by the individual crystallites in a metal section. Since this is almost always impossible of direct measurement, several methods of estimating and expressing the size have been evolved. Most exact methods make use of the microscope. This involves study of a single plane cut at random through the metal. What is seen in the microscopc are polygons, each the cross section of a grain. The diameters or areas of these polygons are then measured and the grain size is expressed as an average diameter, number of grains per unit area, average area per grain, or, rarely, average volume per grain. Rutherford, Abom, and Bain3 have discussed extensively the errors involved when using a plane section to estimate volume. They clearly point out that the tendency is to underestimate the true grain size because of the nature of the measurcment. The A.S.T.M. recommends that measurement be made by comparison with a standard chart, by means of Jeffries' planimetric method4 or Heyn's intercept method. The Society recommends that the notation be in terms of the number of grains per unit area (as is the grain-size number used for steel) or as an average diameter, expressed in inches or millimeters (as for copper and brass). The method of measurement used for this study was comparison with a standard chart, which has been described by P. F. George.5 The chart was constructed by photographing at Ioo diameters a uniform specimen with an average grain diameter of 0.003 in. The average diameter of this specimen was determined by numerous measurements, using both the Jeffries and Heyn methods. The other grain sizes were then obtained by appropriate enlargemcnt of the master sample. Careful comparison of the chart method with other methods on identical samples indicates that though the differences be-

Jan 1, 1945

By C. W. Phillips, R. S. Busk

WITH most cast metals the grain size may vary within wide limits, depending upon the conditions at the moment of freezing. These conditions are subject to control in magnesium-base alloys, by proper melting and superheating techniques, enabling production of quite uniform and fine-grained castings, almost independent of section thickness. However, such variations of grain size as do exist, in common with all metals, are reflected in corresponding changes in mechanical properties. It is the intent of this paper to present data giving the relationship between grain size and mechanical properties. Data are also included on the combined effects of grain size and microporosity. In addition, a short discussion of factors influencing the grain size of sand castings is included. MEASUREMENT OF GRAIN SIZE By grain size is meant the statistical distribution of volumes occupied by the individual crystallites in a metal section. Since this is almost always impossible of direct measurement, several methods of estimating and expressing the size have been evolved. Most exact methods make use of the microscope. This involves study of a single plane cut at random through the metal. What is seen in the microscope are polygons, each the cross section of a grain. The diameters or areas of these polygons are then measured and the grain size is expressed as an average diameter, number of grains per unit area, average area per grain, or, rarely, average volume per grain. Rutherford, Aborn, and Bain3 have discussed extensively the errors involved when using a plane section to estimate volume. They clearly point out that the tendency is to underestimate the true grain size because of the nature of the measurement. The A.S.T.M.. recommends that measurement be made by comparison with a standard chart, by means of Jeffries' planimetric method' or Heyn's intercept method. The Society recommends that the notation be in terms of the number of grains per unit area (as is the grain-size number used for steel) or as an average diameter, expressed in inches or millimeters (as for copper and brass). The method of measurement used for this study was comparison with a standard chart, which has been described by P. F. George.', The chart was constructed by photographing at i00 diameters a uniform specimen with an average grain diameter of 0.003 in. The average diameter of this specimen was determined by numerous measurements, using both the Jeffries and Heyn methods. The other grain sizes were then obtained by appropriate enlargement of the master sample. Careful comparison of the chart method with other methods on identical samples indicates that though the differences be-

Jan 1, 1945

By R. W. Kraft, L. D. Graham

The process of' spheroidization, or more properly coarsening, of Al-CuAl,eutectic alloy specimens with various initial microstructures was studied by quantitative metallographic and X-ray diffraction techniques. By measuring the rale at which specimens with a very fine dispersion of phases (produced by quenching molten droplets of the alloy in water) coarsened it uias determined that the rate-controlling mechanism for coarsening was diffusion, probably of aluminum in the aluminum-rich phase. The lamellae in specimens with a high degree of microstructural and cr-ystallog/uphic anisotropy (produced hy unidirectional solidification of ingots) thickened during heat treatment by recession of the CuAl, platelets from jaulted regzons, yet the specinlens retained a very high degree of. anisotropy after prolonged heat treatments at a temperature within 8°C of the eutectic temperature. In such specimens the crystallographic orientation relationship between the phases remained constant and no change in the crystallographic substructure occurred. Based on these observations a model was developed for the coarsening—or rate of' thicken-ing—oj- the lamellar structures which predicts that the rate of decrease of interface area is proportional to the square of lamellar interface area. Experiments with degenerate and very coarse lamellar microstruc -tures preduced by extremely slow unidirectional solidification) indicate that initial microstructure is a most important factor governing the final micro-structure after heat treatment. The particle size and shape of dispersed phases are important parameters affecting the properties of a wide variety of two-phase materials. As is well-known, varietythe dispersed-phase particles tend to coarsen at appropriately high temperatures because the interface energy of the system is reduced by the concomitant reduction in interface area. The phenomenon of

Jan 1, 1967

By R. H. Olds, B. H. Sage

The transient flow of gases in long pipe lines is a problem of industrial interest. The present discussion deals with the application of the conservation of momentum and material to the transient flow of gas in conduits which are long with respect to their diameter. Solutions of the resulting equations include consideration of variations in friction and specific volume of the fluid as functions of time and position along the conduit. The changes in state along the pipe line are established as a function of time. The methods proposed may be extended to other situations. The flow of compressible fluids under steady conditions' has been considered in detail. Primary emphasis was placed on the development of simple means of taking into account the non-uniform flow' realized in long conduits under such conditions. Binder2 discussed the essential differences between the flow of compressible and uoncompressible fluids. Bonilla" proposed direct methods of solution for equations describing isothermal flow in long pipes. Similar considerations limited to steady flow have been discussed by Ruth.' Palsgrove 5 sugrested a graphical means of solving specific problems relating to the flow of gases in conduits of uniform section. Some of the basic concepts of the flow of a compressible viscous fluid in straight tubes have been described by Kuo.6 Problems of this type require knowledge of the equation of state of the fluid. In many cases it liar been convenient to assume that the fluid follows the relationship ascribed to a perfect gas. The treatment of unsteady flow of compressible fluids is less complete. This state of affairs result* from the fact that the differential equations relating pressure and flow rate with time and position for unsteady flow are nonlinear in character.' Muskat and Wyckoff presented an excellent treatment of the situation in laminar Bow where inertia forces were not of controlling importance. Somewhat earlier Hurst9 discussed the uncteady flow of fluids in petroleum reservoirs. Helhering-ton. MarRoberts. and Huntington'" established experimentally the pressure distribution and accumulative flow rate of natural gas through an unconsolidated sand. Recently Joffe11,12 conhitlcretl the specific problem of the flow of natural gas in relatively long.,. pipe lines for unsteady conditions with emphasis upon the economic feusibility of the storage of gas in such a reservoir. These discussions were based upon approximations of the partial differential equations applying to the condititons of flow. The results were descriptive of the physical situation and indirated the effertiveness of large pipe lines as cyclic storage facilities for natural gas. The advent of analog computers" has increased materially the practicality of solving nonlinear partial differential expressions. Several iterative numerical and graphical methods14,15,16 have been developed to solve nonlinear equations. However, it appears that the pair of simultaneous nonlinear partial differential equations involved in problems of this nature are not directly susceptible to solution by presently available analog computer or formal iterative numerical techniques. Nevertheless. graphical analyses afford a means of obtaining data of engineering value without special equipment. MATHEMATICAL CONSIDERATIONS Since the length of the conduit is large in comparison to the cross section in the cases to be considered, it is possible to treat the characteristics of the flow as independent of position in the cross section of the conduit. This possibility follows since the energy- connected with the velocity profile is small compared to that required to overcome the friction associated with its movement throughout the length of the line. Average values of the pressure. velocity. kinetic energy. momentum, and specific volume may he assigned to the fluid at any particular cross section. From a mathematical viewpoint this may be expressed in the following way for velocity: µ = µ(?X)..........(1) The uncertainties introduced by such assumptions usually are negligible when the ratio of length to diameter is greater than the order of 1.000. On this basis a volume element ma!. be considered to occupy the entire cross section of the conduit. Such an element is presented in Fig. 1.

Jan 1, 1951

By R. H. Olds, B. H. Sage

The transient flow of gases in long pipe lines is a problem of industrial interest. The present discussion deals with the application of the conservation of momentum and material to the transient flow of gas in conduits which are long with respect to their diameter. Solutions of the resulting equations include consideration of variations in friction and specific volume of the fluid as functions of time and position along the conduit. The changes in state along the pipe line are established as a function of time. The methods proposed may be extended to other situations. The flow of compressible fluids under steady conditions' has been considered in detail. Primary emphasis was placed on the development of simple means of taking into account the non-uniform flow' realized in long conduits under such conditions. Binder2 discussed the essential differences between the flow of compressible and uoncompressible fluids. Bonilla" proposed direct methods of solution for equations describing isothermal flow in long pipes. Similar considerations limited to steady flow have been discussed by Ruth.' Palsgrove 5 sugrested a graphical means of solving specific problems relating to the flow of gases in conduits of uniform section. Some of the basic concepts of the flow of a compressible viscous fluid in straight tubes have been described by Kuo.6 Problems of this type require knowledge of the equation of state of the fluid. In many cases it liar been convenient to assume that the fluid follows the relationship ascribed to a perfect gas. The treatment of unsteady flow of compressible fluids is less complete. This state of affairs result* from the fact that the differential equations relating pressure and flow rate with time and position for unsteady flow are nonlinear in character.' Muskat and Wyckoff presented an excellent treatment of the situation in laminar Bow where inertia forces were not of controlling importance. Somewhat earlier Hurst9 discussed the uncteady flow of fluids in petroleum reservoirs. Helhering-ton. MarRoberts. and Huntington'" established experimentally the pressure distribution and accumulative flow rate of natural gas through an unconsolidated sand. Recently Joffe11,12 conhitlcretl the specific problem of the flow of natural gas in relatively long.,. pipe lines for unsteady conditions with emphasis upon the economic feusibility of the storage of gas in such a reservoir. These discussions were based upon approximations of the partial differential equations applying to the condititons of flow. The results were descriptive of the physical situation and indirated the effertiveness of large pipe lines as cyclic storage facilities for natural gas. The advent of analog computers" has increased materially the practicality of solving nonlinear partial differential expressions. Several iterative numerical and graphical methods14,15,16 have been developed to solve nonlinear equations. However, it appears that the pair of simultaneous nonlinear partial differential equations involved in problems of this nature are not directly susceptible to solution by presently available analog computer or formal iterative numerical techniques. Nevertheless. graphical analyses afford a means of obtaining data of engineering value without special equipment. MATHEMATICAL CONSIDERATIONS Since the length of the conduit is large in comparison to the cross section in the cases to be considered, it is possible to treat the characteristics of the flow as independent of position in the cross section of the conduit. This possibility follows since the energy- connected with the velocity profile is small compared to that required to overcome the friction associated with its movement throughout the length of the line. Average values of the pressure. velocity. kinetic energy. momentum, and specific volume may he assigned to the fluid at any particular cross section. From a mathematical viewpoint this may be expressed in the following way for velocity: µ = µ(?X)..........(1) The uncertainties introduced by such assumptions usually are negligible when the ratio of length to diameter is greater than the order of 1.000. On this basis a volume element ma!. be considered to occupy the entire cross section of the conduit. Such an element is presented in Fig. 1.

Jan 1, 1951

By Edward Nichols

As far as known to the writer, no discovery has heretofore been made in the United States of deposits of beauxite, or the hydrated oxide of alumina. The deposit which forms the subject of this note was discovered in Floyd County, Georgia. Numerous "float" specimens, covering an area of about half an acre, indicate the location of the main deposit, which has thus far been opened to an inconsiderable extent only. The excavations show the beauxite to exist apparently as large masses in clay. The formation is Lower Silurian, as determined by the Geological Survey of Georgia. The surface in the immediate vicinity is covered with numerous angular fragments of chert, which is a characteristic rock throughout this formation in Georgia. An examination of the mineral shows it to have the oolitic structure common to several beauxites. It. varies in color from a light salmon to dark red, depending upon its contents of iron oxide. The light-colored specimens are comparatively soft, while the dark mineral is much harder, spots in the latter being

Jan 1, 1888