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By L. W. Kempf, R. S. Archer

The binary aluminum-silicon alloys have certain characteristic advantages which are now well known, and these alloys have come into considerable use during the past several years.' Their field of application has been limited to a certain extent, however, by their low yield point and hardness, low endurance limit, and relatively poor machining characteristics. These properties are improved by the addition of copper, and the ternary aluminum-silicon-copper alloys constitute an important class. The addition of copper decreases the corrosion resistance of the aluminum-silicon alloys and increases specific gravity. Magnesium is a hardening addition which seems to have relatively little effect on corrosion resistance, and which, of course, reduces specific gravity. The object of the work described in this paper was the development of alloys and heat treatments for the production of sand castings and permanent-mold castings having substantially all the advantages of the binary aluminum-silicon alloys together with mechanical properties improved to a degree permitting wider application. Constitution of Alloys Magnesium and silicon combine in aluminum alloys as the compound Mg2Si, which forms a binary system with aluminum. In alloys containing an excess of silicon over that required to form the compound, solidification ends with the freezing at 1022' F. (550' C.) of a ternary eutectic of aluminum, Mg²Si, and silicon. Judging from the horizontal projection of the liquidus surface as given by Hanson and Gayler,² this ternary eut,ectic contains about 13 per cent. silicon and 6 per cent. magnesium. All of the alloys discussed here contain excess silicon, so it

Jan 1, 1931

By H. B. Huntington

Some of the basic problems in understanding elec-tromigration in metals are discussed, along with the attempts that are being made to handle them. One such problem is the effect of the electrostatic forces. It is now acknowledged that the momentum exchange with charge carriers plays generally a dominant role in the driving force but the question remains to what extent the electrostatic force may still be effective. The electromigration of interstitial impurities is also an area which presents some intriguing questions. For the substitutional impurity, moving by the vacancy mechanism under the influence of an electric field, the correlation considerations are somewhat more complex than have been previously recognized. Another problem of basic importance in the calculution from first principles is the strength of the "electron friction" force, say for a simple one-band metal. A related problem growing out of the preceding is the prediction of the direction of the "electron wind" force for metals with band structure involving both holes and electrons. THE term electromigration has come to be used to describe the flow of matter in condensed phases carrying high electronic currents such as metals and alloys, whereas one usually reserves the term electrolysis for situations where the current is largely ionic, particularly in the liquid state such as molten salts. It follows that the mass transport number in electromigration is always very small, of the order of 10-7. Studies of electromigration date back some 30 years but the modern period would appear to date from the work of Seith and Wever1 who in the mid 1950's first incorporated markers to display mass motion relative to the lattice and first suggested that the direction of the mass flow was primarily determined by the sign of the charge carriers. Since that time interest in the field has grown steadily and more rapidly recently as certain technological applications became apparent. Chief of these is certainly the deleterious effects that electromigration can cause, even at relatively low temperature, to current-carrying elements in integrated circuitry.2 These phenomena have been the subject of intense study and considerable ingenuity. On the constructive side electromigration has proved a useful tool in the purification of certain metals.3 The interest of this paper is, however, centered more on the basic aspects of the subject than on its technological applications. That high electric currents should give rise to mass flow in metals and that the driving force should be more directly associated with momentum exchange with the charge carriers than with the electrostatic field are ideas that no longer cause surprise or particular interest. The field has matured to the point where the general concepts are widely accepted and continued progress in basic understanding rests on more detailed and quantitative exploration. It is the purpose of this paper to point out what are some of the current problems. As a result, we expect to raise more questions than we answer. The first of these will be the role of electrostatic forces, if any, in electromigration. A second section will deal with the electromigration of interstitials. A third and final section treats with electromigration of substitutional impurities or of the matrix atoms themselves. ELECTROSTATIC DRIVING FORCE In the conceptual treatments of electromigration it has been customary to write the driving force in terms of an effective charge number Z* and to divide it into two terms F = e£Z* = e£[Zel- z(pd/Nd)(N/p)(m*\m*\)] [1] The first of these represents the electrostatic force under immediate consideration in this section and the second and usually dominating term for metals arises from momentum exchange with charge carriers, commonly called the "electron drag" term. As can be seen it is set proportional to the electrons per atom, z, and the ratio of the specific resistivity of the moving entity to the corresponding resistivity per matrix atom. The (m*/Im*I) factor takes into account the fact that the sign of the charge carrier determines the sign of the driving force. The specific resistivity of the moving entity is averaged over its path. In the case of motion of the matrix atoms by vacancies this gives rise to approximately one-half the resistivity at the saddle point since the scattering power of the atom at its equilibrium position bordering the vacancy differs only slightly from that of a normal matrix atom. Although the formulation of the "electron drag" term in Eq. [I] is based on a highly simplified model for electron defect scattering, the essential features implicit in the expression are common to all the theoretical approaches that have so far appeared in the literature.4-6 As for Zel, most treatments of electromigration have included the quantity as the parameter which measures the direct interaction of the electrostatic field with the ion and equated it to the nominal valence of the latter. However, there has been considerable discussion whether this interaction may not be 0 in many cases.6 If the moving ion is always enveloped by the same distribution of shielding charge, then clearly its motion will not involve any work done by the electric field and one can expect there will be no electrostatic force exerted on such a neutral composite. From this point of view the shielding charge around the ion would be said to be complete and hence the entity within the Debye shielding sphere would be unaffected by the electrostatic field per se. There is, however, the prospect that, as the moving ion progresses, new charge comes in to participate in the shielding action

Jan 1, 1970

By AIME

Lewis E. Young, who will formally assume his duties as President of the AIME at the Annual Meeting in San Francisco in February 1949, was born in Topeka, Kansas, Oct. 1, 1878. Dr. Young received his engineering education at the Pennsylvania State College, where he received the degree of B.S. in Mining Engineering in 1900. In 1904 he received his E.M. degree from Iowa State College, and in 1915 a Ph.D. from the University of Illinois. In 1947, the University of Missouri conferred on Dr. Young honoris causa the degree of Doctor of Engineering. His active career began in the educational field as instructor at Iowa State College, and following that, as professor of mining at the Colorado School of Mines, 1903-1907. While he was at Golden he launched hi: career as consulting mining engineer for various Western companies. Leaving the Colorado School of Mines, Dr. Young returned to Missouri, serving the University of Missouri as director of the School of Mines and Metallurgy at Rolla, 1907-1914. Leaving Missouri he went to the University of Illinois as assistant professor of business organization, 1915-1918, during which period he wrote exhaustive treatises on mine subsidence and mine taxation, which won for him the degree of Ph.D. before mentioned.

Jan 1, 1949

By G. W. Healy, N. R. Griffing

The activity coefficient of sulfur in Cr-Fe-S melts was determined by measuring the values of Ph3Rh,in equilibrium with such melts. The results showed that chromium has a pronounced negative effect on the activity coefficient of sulfur, which up to about 20 pct Cr may be represented by the equation: log f; = - 0.019 pct Cr It was also found that the influence of chromium was not altered by the presence of appreciable amounts of carbon or silicon. The influence of alloying elements on the activity of sulfur in molten iron has been the subject of many investigations; however the effect of one important alloying element, chromium, has not been reported, and the object of the present investigation was to determine its effect on the activity coefficient of sulfur in liquid Fe-Cr-S alloys both in the absence and in the presence of carbon and/or silicon. EXPERIMENTAL PROCEDURE The general method employed consisted of passing mixtures of hydrogen and hydrogen sulfide over the sulfur-containing melt of interest and analyzing the outgoing gas to determine the equilibrium value of which resulted from the reaction shown in Eq. 111. H, (gas) + S (dissolved in melt) = H,S (gas) 111 The activity coefficient of sulfur, fs, was then calculated with Eq. [2] in which K, is the known equilibrium constant of Eq. [I] for dilute solutions of sulfur in iron. Raw materials used in the preparation of the charges included commercial grades of electrolytic iron and chromium and carbon-reduced, acid-treated silicon of 99.9 pct purity. Oxygen in the former presented no problem since it was removed by hydrogen in the normal course of an experiment. Carbon was added in the form of premelted iron-carbon and chromium-carbon master alloys. Sulfur was charged as iron sulfide prepared by first heating powdered iron and sulfur in air in an alumina dish until reaction occurred, and then deoxidizing by melting in a hydrogen atmosphere. Commercially bottled hydrogen and hydrogen sulfide were used after being passed through purification systems containing palladium, "Drierite," and magnesium perchlorate in the case of hydrogen, and "Drierite" alone in the case of hydrogen sulfide. Lamp-grade cylinder argon served as a flushing agent without further purification. Charges weighing from 300 to 500 g were placed in a high-purity alumina crucible of 0250-ml capacity and heated in an argon atmosphere in the induction-heated carbon-tube furnace illustrated in Fig. 1. During heating, a dry hydrogen atmosphere was substituted for argon in order that deoxidation of the charge and flushing out of argon would be accomplished sooner. After the charge melted, a Pt-Pt 10 pct Rh thermocouple contained in an alumina protection tube was immersed in the melt, and the desired melt temperature (usually 1600°C) was established. Higher temperatures up to 1760°C were required for some chromium-rich alloys because of their higher melting points, and in these cases a Pt 6 pct Rh-Pt 30 pct Rh thermocouple was used. The thermocouple output was fed to an automatic controller which provided straight line temperature

Jan 1, 1961

By Wilford Stork

CERTAIN influences of oxygen on iron have been known for many years and it has always been considered one of the worst enemies of the iron and steel founders. Nobody had a good word for it, hence little was done to make use of this oxygen. In all the fields of foundry practice, the desideratum was "melt without oxidation of the metal." In the consideration of the influence of oxygen on cast iron, we must not confuse this condition with oxidized iron caused by poor melting conditions, due to a high bed, heavy charges, low coke ratio, excessive melting rate, high blast, or poor charging. It is admitted that oxygen absorbed by iron melted under these conditions has a deleterious effect on the properties of the iron. The writer has had experience both in the melting under such poor conditions and in remedying these bad conditions and considers the product far inferior to iron melted under normal conditions. As stated by Dr. Richard Moldenke,1 such iron has a higher melting point and high combined carbon, is sluggish, and contains slags and oxides in solution in the liquid, causing slag inclusions and gas occlusions, thus producing defective castings. This oxidized condition cannot be counteracted or removed by any of the known deoxidizers; it can be remedied only by proper melting conditions. Such iron is really burned, whereas the iron considered in this paper was melted under normal conditions with moderate blast, correct bed height, light charges of iron, and low coke consumption and is not in this category at all. In 1914, the late J. E. Johnson, Jr., startled the metallurgists of the world when he published his results on the advantages of oxygen on cast iron.2 His work is so convincing and so logical, in spite of the common and well-established notions on the subject, that nobody has been able to refute a single argument. Such an eminent authority on iron and steel metallurgy as Prof. H. M. Howe has accepted the work in all its details in his latest book3 The work of J. E. Johnson, Jr., has revolutionized

Jan 6, 1919

By E. S. Bumps, W. F. Craig, M. Baeyertz

Metallurgists have looked at fractures macroscopically for many years and have evolved a vocabulary in which such words as "cleavage," "brittle," "shear," "ductile," "granular," "fibrous," and "silky" are used to describe the appearance of the fractured surface; but the meaning of these words in terms of metal structure is not well established. Observations of the structural meaning of "brittle" and "ductile" fractures in plate steels have been made, notably, by Kramer and coworkers1 and by Tipper.2 Grossman3 has studied the fracture of tempered martensite and combinations of ferrite and martensite. Notwithstanding these and other less concerted attacks on the problem, present understanding of fracture rests more on assumptions and logic than on experiment. It is the purpose of this paper to add a little to the growing fund of experimental observations of the nature of fractures in steel. The particular fractures to be described were obtained in conventional impact testing of an ordinary structural steel shape. In impact tests of the Charpy type, the specimens fail in a characteristic manner that depends on the steel and the temperature of testing. With ordinary structural and many other steel products, an appropriate range of testing temperature will cause a considerable change in the energy absorbed before fracture. This change is known as the energy transition and is accompanied, more or less closely, by alteration in the appearance of the fracture. At testing temperatures below the transition, the terms "brittle," "cleavage," or "granular" are used to describe the fracture; above it, "ductile" or "shear" are often used. Within the transition, the fracture changes from "brittle" to "ductile" by a progression in appearance, wherein the "brittle" portion of the fracture becomes restricted to a smaller and smaller central area of the fracture, as the testing temperature is raised and the "ductile" type of fracture is approached. All this is well known to metallurgists. The specimens under consideration are of the conventional V-notch Charpy type. They were taken from a structural steel shape of the following analysis: C Mn P S Si 0.17 0.46 0.009 0.029 0.03 Both longitudinal and transverse specimens were tested and examined. Fig 1 shows the energy values plotted against testing temperatures in the usual way. The curves for both longitudinal and transverse specimens show an energy transition, although the maximum energy absorbed at testing temperatures above the transition is greater in the case of the longitudinal specimens. Fig 2 illustrates the changes in the macroscopic appearance of the fractures that are associated with the energy transitions shown in Fig 1. Macrographs of the fractured surfaces of the specimens have been identified with the fracture ratings at intervals on each fracture curve. The numerical fracture rating on the ordinate of Fig 2 indicates the percentage of the area of each fracture that was considered to be "brittle" on macroscopic observation. Such rating of the fracture type in impact tests is now customary in many laboratories. Hereafter the specimens will be identified by reference to Fig 2 as 90 pct "brittle," 80 pct "brittle," and so on, in accordance with this macroscopic evaluation of the appearance of the fractured surface. The discussion of the fractures is divided into three parts. The first two are concerned with the mode of fracture and its relation to general structural features. As the same metal-lographic features occur in both longi-

Jan 1, 1950

By S. K. Nowak

The lithium solubility limit in solid aluminum was determined by the use of micro-graphic techniques. The solubility limit thus established was shown to be a true equilibrium by checking the reversibility of AlLi phase precipitation and dissolution around the equilibrium temperature. The experimental results fit a straight line by plotting log N(LI) against 1/T. The metallurgical reasons explaining the lack of agreement among previous investigations are discussed. THE solubility limit of lithium in solid aluminum was determined by Shamray and Saldau1 by micrography and by Grube et al.' and also Voss-Kiihler- by measurement of electrical resistivity. Since the addition of lithium induces extremely small changes in the aluminum lattice, X-ray techniques could not be employed for this purpose; in fact, the addition of lithium does not cause an expansion of the lattice as might be expected from a consideration of atomic radii, but causes a small contraction from 4.040 to 4.037A3, 4 when the solvent aluminum is saturated with this element. An analysis of the results from previous investiga-tions'" shows that with improvement of investigation techniques the solubility limit tends toward a lower lithium content. Again, some of the author's own experimental results on the action of atomic hydrogen on A1-Li alloys seemed to indicate that the solubility of lithium should be much lower, i.e., about 0.3 pet at 300°C: instead of 1.15 pet, the lowest published value.4 For the foregoing reasons it was decided to investigate this problem. The aluminum and the lithium used for this purpose were of the highest purity. The lithium solubility limit was determined by metallographic techniques, in particular by the use of a reagent especially developed for the purpose of revealing the AlLi phase. The solubility limit thus determined was shown to be a true equilibrium by checking the reversibility of AlLi phase dissolution and precipitation around the equilibrium temperature. All of the experimental work was carried out in 1951 at the Centre d'Etudes de Chimie Metallur-gique at Vitry, France, under the direction of Georges Chaudron.

Jan 1, 1957

By H. W. Young

DEVELOPMENT of high-tension outdoor substations during the past few years has been due primarily to economic reasons. The demand for power in small communities could not be met with the conventional and 1 FIG. 1.-33,000-VOLT STEP-UP OUTDOOR AIR-BREAK SWITCH AND SUBSTATION INSTALLATION OUTSIDE OF A POWERHOUSE GENERATING AT 2300 VOLTS STEPPING UP TO 33,000. TWENTY-ONE COAL MINES ARE SUPPLIED FROM LINES LEADING FROM THIS INSTALLATION. comparatively expensive indoor types unless the rate for service was materially increased. That the various problems incident to development have been solved successfully, it is only necessary to point to the

Jan 9, 1919

By Sandip K. Mitra, John E. Dorn

The Basinki-modified Seeger equation for deformation of metals by means of thermally activated intersection of dislocations was used to ascertain the various factors responsible for the strain hardening of poly crystalline aluminum and a series of a solid solutions of magnesium in aluminum. The analyses were based principally on the rate of change of strain rate with stress and the Cottrell-Stokes ratio. From measurements of these quantities on a series of strain-hardened states, the force displacement diagram for intersection, the density of dislocations in the entanglements, and the contributions of the athermal local stress and long-range stress interactions were deduced. Poly crystalline aluminum was observed to have the same force-displacement diagram for intersection as single aluminum crystals, and the corresponding diagram for the magnesium alloys differed in a manner that suggested that small amounts of magnesium may decrease slightly the stacking fault energy of aluminum. Although poly crystalline aluminum had about the same initial density of dislocations as the single crystals, the density of dislocations increased much more rapidly with strain in the polycrystals. This factor and the higher back stresses generated in the poly crystalline aluminum were the major factors responsible for the higher strength of the poly crystalline aluminum, As the magnesium content of the alloys was increased, the initial density of the dislocations also increased. Most of the alloy strengthening arose from this factor; alloying effects due to short-range order strengthening, Suzuki locking, Cottrell pinning, and so forth, were estimated to be quite small. The gveater rate of strain hardening in the alloys was deduced to be due primarily to the greater increase in the density of the dislocations with strain as the magnesium content was increased. It is the purpose of the present investigation to shed additional light on the average plastic behavior of a grain in a polycrystalline aggregate, by analyses, based on dislocation theory, of appropriate experimental test results. These deductions when compared with those from single-crystal data will then serve to illustrate the major items of difference between the plastic behavior of single crystals and the average behavior of a grain in a

Jan 1, 1963

By R. A. Harrington, H. R. Nelson

The: structure of anodic films formed on aluminum and other metals under varied conditions is not well known despite the wide use of such films both as protective coatings and as the dielectric medium in electrolytic condensers. The present work was undertaken as a survey of the possibilities of electron diffraction in the investigation of anodic films, especially in comparing the properties of anodic films formed under different sets of conditions and subjected to various subsequent treatments. In addition, an effort has been made to compare surface films formed on aluminum by anodic treatment with surface films formed by heating, immersion in chemicals, etc. The elcctron diffraction method in many cases has been successfully applied to the study of thin surface films. Its principal advantage is that it can be used without removing the films from the base material upon which they have been formed. The low penetrating power of electrons, in the "reflection" diffraction method which has been used in this work, prevents the appearance of diffraction patterns from substances at depths greater than about 100 Angstrom units (lop6 cm.). Different investigations of the structure of anodic films have showll widely varying results, depending on the methods used in preparing the films. Apparently under some conditions these films are crystalline and under other conditions they are amorphous, and it has been difficult to say which type of structure will be found in any particular case. Schmid and Wassermann's1 X-ray diffraction patterns of eloxal‡ films show two broad, diffuse bands, which these investigators attribute to finely divided cubic y-Al2O3.§ Burgers, Claassen, and Zernicke³ obtained sharp X-ray

Jan 1, 1940

By R. A. Harrington, H. R. Nelson

The: structure of anodic films formed on aluminum and other metals under varied conditions is not well known despite the wide use of such films both as protective coatings and as the dielectric medium in electrolytic condensers. The present work was undertaken as a survey of the possibilities of electron diffraction in the investigation of anodic films, especially in comparing the properties of anodic films formed under different sets of conditions and subjected to various subsequent treatments. In addition, an effort has been made to compare surface films formed on aluminum by anodic treatment with surface films formed by heating, immersion in chemicals, etc. The elcctron diffraction method in many cases has been successfully applied to the study of thin surface films. Its principal advantage is that it can be used without removing the films from the base material upon which they have been formed. The low penetrating power of electrons, in the "reflection" diffraction method which has been used in this work, prevents the appearance of diffraction patterns from substances at depths greater than about 100 Angstrom units (lop6 cm.). Different investigations of the structure of anodic films have showll widely varying results, depending on the methods used in preparing the films. Apparently under some conditions these films are crystalline and under other conditions they are amorphous, and it has been difficult to say which type of structure will be found in any particular case. Schmid and Wassermann's1 X-ray diffraction patterns of eloxal‡ films show two broad, diffuse bands, which these investigators attribute to finely divided cubic y-Al2O3.§ Burgers, Claassen, and Zernicke³ obtained sharp X-ray

Jan 1, 1940

By D. E. Moore

The strength of a natural serpentinite gouge was measured at 400°C and an effective pressure of 100 MPa. The strength of the gouge decreased with increasing pore pressure to 50 MPa and then was nearly constant between 50 and 125 MPa. The samples at 50-125 MPa pore pressure slid stably, whereas those at 3-25 MPa pore pressure showed stick-slip behavior. Lengthening the pre-heating time to 72,000 s of samples at 100 MPa pore pressure led to increases in both the strength and the likelihood of sliding unstably. With still longer pre-heating times, the strengths decreased again and sliding once more became stable. The strength of the gouge at 3 MPa pore pressure was unaffected by changes in pre-heating time. A possible explanation for the results is that excess pore pressures are being generated in the gouge, causing the true effective pressure to be lower than the apparent value.

Jan 1, 1984

By Herman Dykstra, Irving Fatt

Relative wetting phase permeabilities calculated from capillary pressure-saturation data are compared with measured relative permeability data. The equation relating relative permeability to capillary pressure-saturation data is derived by assuming that a porous medium is analogous to a bundle of capillary tubes. The equation includes a term to correct for the difference between fluid path length and length of core. Relative oil permeability data in the water-oil-gas system are presented, and it is shown that if the water is considered part of he rock matrix, the relative oil permeability curve is typical of a wetting phase relative permeability curve. Apparatus for measuring two and three-phase relative permeabilities are described. INTRODUCTION The difficulty in measuring relative permeability of cores has made it desirable to have a correlation between relative permeability and some more easily measured property of porous media. Such an easily measured property is the capillary preisure-saturation relation. In the past there has been a tendency to separate the capillary pressure concept from the very complex pore geometry and to consider that the capillary pressure-saturation curve give? only some characteristic distribution of interfacial curvature between two fluids.' Recently, however, it has been realized that if capillary pressure data are to yield information concerning pore size distribution2 and fluid flow in porous media. the pore must be assumed to have a simple shape such as a cylinder or a sphere. Childs and George' showed that relative water permeability could be calculated from the capillary pressure-water saturation curve by assuming that the pores are cylinders in which the fluid flowing obeys Poiseuille's Law, and that the capillary preisure curve indicated the size and number of pores. Purcell5 derived an equation relating the permeability of a porous medium to the capillary pressure curve by assuming the porous medium to he analogous to a bundle of capillary tubes. Gates and Lietz6 calculated relative permeability by an equa-tion derived from Purcell's equation. In this paper an equation is derived giving the relative water permeability as a function of water saturation by as-sulning that the core sample can be represented by a bundle of capillary tubes in which the fluid path length is not the same as the bulk length, and in which the fluid path length varies with saturation. THEORY For a bundle of N capillary tubes the flow through dN tubes will be dQ = qav dN ..........(1) where Q is the total flow rate through all the tubes and q., is the aberage flow rate through the tubes in the interval dN. If the interval dN is made small the average flow rate through a tube in the interval dN is given by Poiseuille's Law, 8 nl where ?P is the pressure drop across the tube of length 1 and radius r, and µ is the viscosity of the fluid. Substituting for qav in Equation (1), dQ =pr4 ? P/8µl dN.........(3) Darcy's Law for linear flow of an incompressible fluid in a porous medium is Q = KA?P/µL...........(4) where K is the permeability and ?P is the pressure drop across a bundle of tubes which has replaced the porous medium of length L and cross-sectional area A. Differentiating Darcy's Law with A, ?P, µ, and L constant, dQ = A?P/µL dK.........(5) Equating (3) and (5) gives dK------------dN.........(6) 8Al If the pores are assumed to be cylinders dV =pr2ldN..........(7) where V is the volume of flowing fluid in the pores. Substituting for dN in Equation (6) gives dK = —dV..........(8) 8AI' By definition the saturation, S, of the core is v v S =V/Vp..........(9) Vv -PAL

Jan 1, 1951

By Irving Fatt, Herman Dykstra

Relative wetting phase permeabilities calculated from capillary pressure-saturation data are compared with measured relative permeability data. The equation relating relative permeability to capillary pressure-saturation data is derived by assuming that a porous medium is analogous to a bundle of capillary tubes. The equation includes a term to correct for the difference between fluid path length and length of core. Relative oil permeability data in the water-oil-gas system are presented, and it is shown that if the water is considered part of he rock matrix, the relative oil permeability curve is typical of a wetting phase relative permeability curve. Apparatus for measuring two and three-phase relative permeabilities are described. INTRODUCTION The difficulty in measuring relative permeability of cores has made it desirable to have a correlation between relative permeability and some more easily measured property of porous media. Such an easily measured property is the capillary preisure-saturation relation. In the past there has been a tendency to separate the capillary pressure concept from the very complex pore geometry and to consider that the capillary pressure-saturation curve give? only some characteristic distribution of interfacial curvature between two fluids.' Recently, however, it has been realized that if capillary pressure data are to yield information concerning pore size distribution2 and fluid flow in porous media. the pore must be assumed to have a simple shape such as a cylinder or a sphere. Childs and George' showed that relative water permeability could be calculated from the capillary pressure-water saturation curve by assuming that the pores are cylinders in which the fluid flowing obeys Poiseuille's Law, and that the capillary preisure curve indicated the size and number of pores. Purcell5 derived an equation relating the permeability of a porous medium to the capillary pressure curve by assuming the porous medium to he analogous to a bundle of capillary tubes. Gates and Lietz6 calculated relative permeability by an equa-tion derived from Purcell's equation. In this paper an equation is derived giving the relative water permeability as a function of water saturation by as-sulning that the core sample can be represented by a bundle of capillary tubes in which the fluid path length is not the same as the bulk length, and in which the fluid path length varies with saturation. THEORY For a bundle of N capillary tubes the flow through dN tubes will be dQ = qav dN ..........(1) where Q is the total flow rate through all the tubes and q., is the aberage flow rate through the tubes in the interval dN. If the interval dN is made small the average flow rate through a tube in the interval dN is given by Poiseuille's Law, 8 nl where ?P is the pressure drop across the tube of length 1 and radius r, and µ is the viscosity of the fluid. Substituting for qav in Equation (1), dQ =pr4 ? P/8µl dN.........(3) Darcy's Law for linear flow of an incompressible fluid in a porous medium is Q = KA?P/µL...........(4) where K is the permeability and ?P is the pressure drop across a bundle of tubes which has replaced the porous medium of length L and cross-sectional area A. Differentiating Darcy's Law with A, ?P, µ, and L constant, dQ = A?P/µL dK.........(5) Equating (3) and (5) gives dK------------dN.........(6) 8Al If the pores are assumed to be cylinders dV =pr2ldN..........(7) where V is the volume of flowing fluid in the pores. Substituting for dN in Equation (6) gives dK = —dV..........(8) 8AI' By definition the saturation, S, of the core is v v S =V/Vp..........(9) Vv -PAL

Jan 1, 1951

By T. Lane Carter

It is a curious fact that while in our Transactions there are papers dealing with mining-districts in all parts of the world, in Europe, Asia, Africa, and Australia, there is not one which describes the mining possibilities of Nicaragua, our near neighbor. To be most interested in distant objects, like the moon, and to neglect what lies at our feet, appears to be a trait of human nature. The neglect of Nicaragua is not confined to the American Institute of Mining Engineers. In no other transactions am I able to find papers dealing with mining in Nicaragua, some parts of which are as much in need of discovery and research as the North Pole. I hope this paper will be the precursor of many others to be printed in our Transaclions, dealing not only with the miniilg possibilities of Nicaragua, but with the whole of Central America, where there are vast areas a,waiting skill and capital for their development. Much of this capital and skill should come from the United States in the future, although it is probable that European capitalists, when they appreciate fully the possibilities, will investigate more and more the mining-resources of Nicaragua and ot'her Central American republics. Fig. 1 is a sketch-map of Nicaragua showing the principal mining-districts. 11. History. Mining in Nicaragua did not begin yesterday. It was commenced by civilized man when the Spanish conquerors pene-' trated into the interior and forced the natives to procure the precious metal for them. It is strange that the Spaniards did not find more gold, and work on a scale as extensive as in Colombia and other parts of South America. Probably in Nicaragua the Indians covered up most of the rich prospects

Jan 1, 1911

By M. J. McPherson, R. Venkataramani

R. Venkataramani (Assistant Professor of Mining Engineering, Dept. of Mining, The Pennsylvania State University, University Park, Pa.)-Y. J. Wang and L. W. Saperstein are to be congratulated for their paper on the computer solution of ventilation problems. The limitations on the problem size to be solved by the program (Appendix II) has been outlined in the paper. I would like to add the following additional limitations of this computer program: The dimensions of the variable J1and J2 should be changed to J, (550) and J2 (550) to handle problems containing more than 400 branches, and up to 550 branches. If there are a large number of branches common to the various meshes, another limitation on the problem size will be the dimension of the variable NA. While a higher-order polynomial fitting for the fan characteristic data points is more rigorous, a quadratic relation, if linear interpolation between the points is inadequate, will result in saving computing time without much loss of accuracy. Of course, this can be handled by minor modifications to the existing polynomial fitting routine in the program. M. J. McPherson (Dept. of Mining Engineering, University of Nottingham, Nottingham, England)-The

Jan 1, 1972

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 Keith Sutherland

AEROFLOAT 25 is a complex mixture of free cresylic acid with aryl substituted dithiophosphoric acids, sulphides, disulphides, etc. Its complete composition has not been published by the makers or patentees. It is prepared1 by the reaction between phosphorus pentasulphide and carefully selected cresylic acid. We have been informed that this acid contains no phenol and very little cresol, and that it is rich in the higher alkyl phenols, particularly the xylenols. The reaction between a phenol ROH and phosphorus pentasulphide may produce compounds of the following type:2 (i) RO S P Diaryldithiophosphoric acids RO SH (ii) R-SH Thiophenolic compounds (iii) R-S-R Diaryl sulphides (iv) R-S-S-R Diaryl disulphides (v) Substituted thianthren compounds Except for the simplest type, the thiophenols (ii), the boiling points of these compounds lie above 300° C. The amounts of the thianthren compounds formed from the five xylenols (if all these are present) will vary according to the position of the substituents. In an attempt to ascertain something of the nature of the reagent, fractional distillation under atmospheric pressure was undertaken. At the outset, hydrogen sulphide was freely evolved, and-particularly below 200° C.-the fractions had the strong odor characteristic of the

Jan 1, 1939

By Haley, D. F.

WHEN operations were first started at Climax in 1917 by the Climax Molybdenum Co., they were pioneering in the molybdenum industry for little was known relative to the uses of molybdenum or the metallurgy of molybdenite concentration. Concentration of molybdenite is relatively simple today but in 1916, when the Climax deposit first attracted attention, it presented serious difficulties. Little was known, in fact, even about the assaying of such low-grade molybdenum ores. Mine samples were sent to at least a dozen of the best laboratories in the United States and average values reported varied from 0.4 per cent to 1.0 per cent MOS2. Owing to the wide variations in MoS2 content obtained from reliable chemists, the actual value of the ore was most uncertain. This variation occurred repeat¬edly over a period of six months in 1917. It was finally decided, as a last resort, to cut several tons of sample from the tunnel and have a mill test made, using the recovered MoS2 per ton as the grade of the ore, for a small error in the assaying of the concentrate would not materially affect the results. These mill tests were made by the General Engineering Co. (Callow) at Salt Lake City. The results proved an ore of commercial grade and indicated the flotation process for the best metallurgy. Based upon these tests, the decision was made to build a 200-ton flotation plant. At this time, the art of flotation was

Jan 1, 1946

By Harold W. Aldrich, Walter G. Scott

The leaching process of the Inspiration Consolidated Copper Co. is based upon the solubility of oxidized copper in sulfuric acid and the solubility of sulfide copper, largely in the form of chalcocite, in ferric sulfate solution. This necessitates the carrying of a rather large amount of iron in solution. The ferric sulfate is regenerated from ferrous sulfate by the oxygen given off at the anode during electrolytic precipitation of the copper. In September, 1924, excavation was started at Inspiration, Arizona, for the construction of a plant to treat 7500 tons of ore per day. When the plant was begun, the fact developed that by a minor change in the height of the overflow on the leaching tanks, 9000 tons could be charged into each tank and treated satisfactorily. This determined the maximum capacity of the plant as 9000 tons per day. The first ore was charged in October, 1926, and there are now available the records of five complete years of operation; namely, 1927 to 1931, inclusive. The original estimate of copper content of the ore to be mined for this plant was 1.19 per cent, of which 0.77 per cent was as oxide and 0.42 per cent as sulfide. From the metallurgical results obtained at the 35-ton pilot plant, it was estimated that a 90.0 per cent extraction of the oxide copper and a 75.0 per cent extraction of the sulfide copper could be made. It was estimated that the tailing would carry 0.182 per cent total copper, resulting in a

Jan 1, 1934