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By W. R. Purcell, C. S. Brooks

The internal surfaces of rocks which are in contact with interstitial fluids are known to influence in some degree the recovery of hydrocarbons from pay zones. Despite the admitted importance of the influence of solid surfaces on hydrocarbon recovery, little information is available concerning the extent of surface of reservoir rocks. In this paper a description is given of the apparatus and procedure employed in the determination of the surface areas of sedimentary rocks, and values are reported for a variety of sandstone and limestone cores. In addition, consideration is given to the Kozeny equation, which relates surface area to porosity and permeability. A colliparison is made between the surface areas as calculated from this equation and the geometrical areas of a series of packs of spherical glass beads. Also, for a group of sandstone cores. Kozeny areas are compared with surface areas as determined by the gas adsorption method employed in this investigation. INTRODUCTION It has long been recognized that many processes which are of importance to hydrocarbon production are controlled in some degree by the extent of the surface of the reservoir rock through which the hydrocarbons move. For example, the recovery efficiency that is obtained in a given reservoir is certainly determined in part by the action of interfacial forces between the reservoir fluids and rock, and this action is influenced in turn by the extent of solid surface. Despite the admitted importance of surface effects to problems of petroleum recovery, little information is available concerning the extent of surface of reservoir rocks." It is the purpose of this paper to describe an apparatus which has been employed for the measurement of the surface areas of rock samples and to present the values which have been obtained for a variety of sandstone and limestone cores. In addition, the relationship of surface area to permeability and porosity, as given by the Kozeny equation, will be discussed. METHOD OF MEASURING SURFACE AREA The method of determining surface areas as employed in this work has previously found wide use in studies of porous solids such as catalysts. The method involves the measurement of the amount of physical adsorption of an inert gas, such as nitrogen or argon, on the bare surface of the solid at reduced pressure and constant temperature near the normal liquefaction temperature of the gas. With the aid of the theory of isothermal adsorption as developed by Brunauer, Emmett, and Teller,' it is possible to ascertain the amount of gas (and hence the number of molecules) which is required to cover the solid surface with a single layer of molecules. From a knowledge of the covering area per molecule the total surface ares of the solid can be computed. Since the Brunauer. Emmett, Teller (BET) theory has been adequately discussed elsewhere: it will suffice here merely to present their final equation as ordinarily employed for surface-area calculations. This equation relates the volume of gas, V, which is adsorbed at pressure, P, to the liquefaction pressure, Po, of the gas, and to the volume of gas, V.,, that is required to form a monomolecular layer: In this equation C is a quantity which is related to the heats of adsorption and liquefaction of the gas; for a particular solid-gas system at Constant temperature, C is considered to have a constant value. The basic adsorption data can be presented in the form of Equation (1) by plotting the quantity P/V(Po- P) as a func-

Jan 1, 1952

By R. Hogg, R. Schaller, P. Luckie

OVERVIEW This paper is a review of two fine particle processing unit operations - classification and mixing. It may appear that these two processes have nothing in common. In fact, the simplified symbols used to represent them on flowsheets - a tipped equilateral triangle such that the base lies along the vertical - are totally reversed. For classification, a splitting action, the apex of the tipped triangle is to the left of the vertical base. A horizontal flow arrow indicating input is drawn to the apex while two horizontal flow arrows indicating outputs are drawn from the top and bottom of the vertical base, respectively. On the other hand, for mixing, a blending action, the apex of the tipped triangle is to the right of the vertical base. Two horizontal flow arrows indicating inputs are drawn to the top and bottom of the vertical base, respectively, while a single horizontal flow arrow indicating output is drawn from the apex. Classification is the process whereby a collection of particles is separated into two or more portions differing in some physical or chemical property. Mixing is the process whereby two or more portions of particles differing in some physical or chemical property are combined into a collection of particles. The common bond that links them together in the same review is the fact that they both require dispersion of the particles in order to achieve successfully their individual objectives.

Jan 1, 1980

By W. J. Reagan

A survey of the literature on bottom-cast practice gives but Scant information as to some of the real facts concerning this most int'eresting method of steel manufacture, and some of the information available is very misleading. An exceptionally good description of this met,hod of pouring or teeming is to be found in an English publication2 on the heterogeneity of steel ingots. Quoting from this paper: (a) With bottom teeming, the metal rises steadily and progressively in the mold with the minimum possible agitation, the main force of the stream coming from the ladle being broken down or retarded by the down gate or runner. Further, the stream of metal from the ladle, under these conditions of casting, is invariably maintained at a much more continuous rate and is steadier than with top teeming. (b) In view of the facts referred to in (a) it follows that with bottom teeming the metal is not exposed to atmospheric oxidation to anything like the same degree as with top teeming. In this paper it is intended to detail briefly some of the advantages of bottom-cast practice and to discuss the possibilities of iron-oxide control in the basic open-hearth furnace. A description of the type of charge, ingot rnold set-up, etc., is found in detail in an earlier paper.3 Design of Ingot Molds In any kind of steel manufacture, ingot-mold design is important. L. H. Nelson4 lists in the order of their probable importance the following factors as influencing most the solidification of the ingot:

Jan 1, 1934

By F. V. Lenel

Resistance sintering under pressure is a method of hot pressing in which a powder compact is subjected to pressure and simultaneously heated by passing a low voltage high amperage current through it. Equipment for this process is described. Its basic characteristics such as resistance requirements for powders and compacts, temperature distribution in compacts, and gas reactions during resistance sintering are discussed. Examples of the sintering process in compacts made of a single metal or an alloy powder and in compacts made of mixtures of powders are presented. Potential commercial applications of the process are evaluated. THE usual sequence of operations in commercial powder metallurgy is to compact metal powders in a die at room temperature and sinter the compact subsequently without applying pressure while the compact is in the sintering furnaces. In hot pressing, on the other hand, the compacting and the sintering are combined. The loose powder, or in many cases a cold formed compact, is inserted into the die which is held at the hot pressing temperature, the compact is left in the die until it attains its temperature, and then pressure is applied and maintained for a given length of time. The die may be heated by surrounding it with a suitable furnace, by high frequency induction heating, or by passing current through the die. In hot pressing, compacts of high density and good mechanical properties can be produced in a relatively short time. One of the principal difficulties in hot pressing is the lack of suitable die materials which will have adequate strength at the hot pressing temperature. This difficulty can be overcome at least partially by heating only the material to be hot pressed without heating the die directly. This can be done by passing a low voltage high amperage current through the material and simultaneously subjecting it to pressure. Either loose powders or compacts can be hot pressed by this method in which the desired temperature is produced by the power dissipated in the metal powder. This method of hot pressing has been termed "electrical resistance sintering under pressure." The most significant differences between this operation and conventional hot pressing are: 1—The sintering times are very short, usually a fraction of a second and at most a few seconds. 2—The powder and die are initially cold. 3—Heat is generated within the powder itself and not conducted in from the die. 4— The pressure used is high. 5—Cooling following sintering is rapid, amounting to a quench. Resistance sintering of metal powders under pressure has been suggested repeatedly. In 1933, G. F. Taylor' proposed an apparatus which consisted of an insulating tube made of glass, or a ceramic filled with the powder to be pressed, and plungers above and below the powder. The powder was to be heated by passing an electric current through it and pressure was then applied. The apparatus was intended principally for hot pressing cemented carbides. Although the principle of resistance sintering under pressure is clearly shown in this patent, few details are given. A sintering period of a second or a fraction of a second, which is terminated by the operation of an inertia switch, is mentioned but no values for current density are mentioned. Low pressures, such as atmospheric pressure or a somewhat higher pressure exerted through a lever, are suggested. W. D. Jones' discussed electrical resistance sintering under pressure and proposed using resistance welding apparatus for this purpose. In a patent issued in 1944, G. D. Cremera described a method of electrical resistance sintering under pressure using resistance welding apparatus which was to be applied mostly to nonferrous metals such as copper, brass, bronze, and aluminum. Current densities of 400,000 amp per sq in., sintering times of 1 and 2 cycles of 60 cycle current, and pressures of 5 to 10 tsi are proposed. Cremer suggested using an

Jan 1, 1956

By William E. Ford, Edward Salisbury Dana

Secondary Twinning. - When there is reason to believe that the twinning has been produced subsequently to the original formation of the crystal, or crystalline mass, as, for example, by pressure, it is said to be secondary. Thus the calcite grains of a crystalline limestone often show such secondary twinning lamella?. The same are occasionally observed (Ilc, 001) in pyroxene crystals. Further, the polysynthetic twinning of the triclinic feldspars is often secondary in origin. This subject is further discussed on a later page, where it is also explained that in certain cases twinning may be produced artificially in a crystal individual - e.g., in calcite (see Art. 282).

Jan 1, 1922

By Ralph V. Higgins

This paper concerns the magnitude of the amount of supersaturation that occurs in an underground reservoir during the flow of oil and gas to wells and to the amount of undersaturation that occurs during repres-suring of an oil reservoir where some effective permeability to gas exists. The study is based on earlier laboratory findings of other investigators on the rate of diffusion of gas in oil as a function of the depth of oil. Utilizing these relationships and the principles of reservoir mechanics, a quantitative estimate of undersaturation and super-saturation was calculated. The results showed that the diffusion of the gas is rapid enough that for all practical purposes no supersaturation exists during the flow of oil to wells or undersaturation during repressuring in reservoir sands having some effective permeability to gas. The reason diffusion of the gas virtually keeps the oil saturated is the long time required in radial flow for oil to reach the well and the slow rate at which pressure in reservoirs is increased during repressuring. INTRODUCTION Knowledge of the phase relationships during flow of gas and oil in an underground reservoir is essential to operating the reservoir in the most efficient manner. In material-balance calculations and in fluid-flow studies, the oil is assumed to contain all the gas that it will dissolve at given temperature and pressure. Pressure-volume-temperature relationships are normally obtained in the laboratory using "bottom-hole" or combined samples of the reservoir fluids. In such laboratory determinations equilibrium is obtained between the oil and gas in the pressure cells by mechanical agitation. During the flow of oil and gas in reservoirs, however, no comparable agitation occurs to mix thoroughly these fluids to aid in effecting equilibrium between the two phases. During repressuring of a partly depleted underground reservoir, the gas is usually injected into the reservoir faster than the oil can absorb it; consequently, the oil is undersaturated. On the other hand, as the oil flows through the reservoir to the wells during producing operations the pressure decreases faster than the gas in solution can diffuse through the oil to the gas phase. The oil therefore is supersaturated with gas. Where the oil is undersaturated, gas diffuses away from the gas-oil interface, and where it is supersaturated the gas diffuses toward the interface. In either case the gas moves from a higher to a lower saturation. This report contains the results of a study of the factors influencing the degree of nonequilibrium of the phase relations of oil and gas in porous mediums during the flow of oil through reservoirs to wells and also during the injection of gas into partially depleted sands. Data from an underground reservoir are presented and the degree of supersaturation during the flow of the oil through the reservoir to the well is approximated. Also data from another reservoir are used and the degree of undersaturation during the repressuring operation is calculated. In addition, the flow rates of oil in laboratory experiments and in underground reservoirs are compared, as data from the laboratory are often used to interpret events in the reservoir, and the rates of flow influence appreciably the degree of nonequilibrium. Much of the contents of this report was prepared in 1943; but, because of other activities during and since the war, the manuscript was left untouched until 1952, when it was decided to include an estimate of the amount of undersaturation during repressuring as well as supersaturation during flow.

Jan 1, 1955

By E. Stansfield

THIS test was described in a privately circulated First Progress Report on Slacking Characteristics of Coal, by A. C. Fieldner and W. A. Selvig, May 1, 1928. The test was described in detail in U. S. Bureau of Mines Report of Investigation 3055, in November, 1930.1 The test, in brief, is conducted as follows: A sample of freshly mined coal consisting of 18 to 25 pieces approximating 1 ¼ cubes, and weighing 500 to 600 grams, is taken for the test. The sample is subjected to a "blank sieving" of carefully regulated degree, on an 8-in. circular sieve with 0.263-in. square openings; and the undersize and oversize weighed. The oversize is placed on a sheet-iron pan and dried for about 24 hr. in an A.S.T.M. air-drying oven maintained at 30° to 35° C. through which a current of warm air is drawn. The sample is then cooled to room temperature and immersed for one hour in water at the same temperature. The water is then drained off, the sample dried for 24 hr. as before, cooled, sieved as before, and the oversize and undersize weighed. The percentage weight of the undersize, is calculated and reported as the first cycle loss. This loss, corrected by subtracting the percentage loss in the blank sieving, is termed the slacking index. The sample may be subjected to further cycles of wetting, draining, air-drying, sieving and weighing. In a letter (August, 1932) W. A. Selvig approved making the blank sieving on a duplicate sample, rather than on the sample used for the test, where sufficient coal was available. This method is now employed in these laboratories. The accelerated weathering test has been employed in the labora-tories of the Research Council of Alberta, at Edmonton, since 1928, but not found entirely satisfactory as repeat determinations with samples taken from the same or adjacent mines frequently showed serious differ-ences. Differences must be expected as the coal may vary in the seam, and the selection of a typical set of lumps approximating 1 ¼ -in. cubes

Jan 1, 1934

By K. C. Gilbart, E. Stansfield

This test was described in a privately circulated First Progress Report on Slacking Characteristics of Coal, by A. C. Fieldner and W. A. Selvig, May 1, 1928. The test was described in detail in U. S. Bureau of Mines Report of Investigation 3055, in November, 1930,1 The test, in brief, is conducted as follows: A sample of freshly mined coal consisting of 18 to 25 pieces approximating 1 1/4 cubes, and weighing 500 to 600 grams, is taken for the test. The sample is subjected to a "blank sieving" of carefully regulated degree, on an 8-in. circular sieve with 0.263-in. square openings, and the undersize and oversize weighed. The oversize is placed on a sheet-iron pan and dried for about 24 hr. in an A.S.T.M. air-drying oven maintained at 30" to 35" C. through which a current of warm air is drawn. The sample is then cooled to room temperature and immersed for one hour in water at the same temperature. The water is then drained off, the sample dried for 24 hr. as before, cooled, sieved as before, and the oversize and undersize weighed. The percentage weight of the undersize is calculated and reported as the first cycle loss. This loss, corrected by subtracting the percentage loss in the blank sieving, is termed the slacking index. The sample may be subjected to further cycles of wetting, draining, air-drying, sieving and weighing. In a letter (August, 1932) W. A. Selvig approved making the blank sieving on a duplicate sample, rather than on the sample used for the test, where sufficient coal was available. This method is now employed in these laboratories. The accelerated weathering test has been employed in the laboratories of the Research Council of Alberta, at Edmonton, since 1928, but not found entirely satisfactory as repeat determinations with samples taken from the same or adjacent mines frequently showed serious differences. Differences must be expected as the coal may vary in the seam, and the selection of a typical set of lumps approximating 1 1/4-in. cubes

Jan 1, 1934

By L. C. Morganroth

CARBONIFEROUS CLAYS FROM a geological standpoint, but scant attention has been paid to fire-clay beds. Only within the last few years have they been the subject of individual investigation, prior to this time having been considered only in their relation to coal seams. While the relative importance of coal and fire clay is still immeasurably in favor of coal, yet an industry as large as that of fire clay is entitled to a measure of attention. A discussion of the Carboniferous clays is practically a discussion of the clay beds in the Appalachian basin, since more than 90 per cent. of these clays mined are from this region. The clays are confined to the northern end of the basin, or the States of Pennsylvania, Ohio, Kentucky, Maryland and West Virginia, ranking in importance about in the order named. The clay deposits of the Carboniferous period have been divided into two classes; those found in the Pottsville conglomerate series of rocks, and all those that are found in the formations above, for the reason that the clay beds above the Pottsville series all resemble each other in properties, composition and appearance, and all are distinctly different from the bed found in the Pottsville formation. The bed of clay found in the latter formation is unique in that flint clay is practically restricted to it. (A variety of flint clay is occasionally found in these upper deposits but this is in such small amounts as to be negligible.) Carboniferous clays occur between stratified rocks; sandstones, limestones, etc., in the same manner as coal veins. They are often accompanied by a coal vein although where the clay is of a workable thickness the coal is generally too thin to work. The clay beds are sometimes known by the name of the coal seam at which horizon they occur. Clay beds may be from a few inches up to 20 ft. in thickness. They may consist of all soft clay all flint or both soft and flint.

Jan 2, 1916

By E. T. Turkdogan, P. Grieveson

Experimental results are given for the rate of oxidation of ferrous iron to ferric iron in pure molten iron oxide by carbon dioxide + carbon moloxide mixtures at 1550°C. It is shown that the rate-controlling process is the interdiffusion of iron and oxygen atoms within the melt. The inter-diffusivity of iron and oxygen in the melt is obtained from the results and the value of (5.0 * 1.0) x 10-5sq cm per sec is recommended for the temperature of 1550°C. Similarly, it is also found that the rate of reduction of molten iron oxide is con -trolled by diffusion in the melt; however, apparent interdiffusivity values from these experiments are 10 to 20 pct higher than those obtained in the oxidation experiments, by virtue of convection arising from density difference. The results of the oxidation experintents are used to calculate an estimated self-diffusivity of iron in molten iron oxide of (1.5 * 0.5) x sq cm per sec. BECAUSE of the industrial importance of iron oxides, the study of the kinetics of both the reduction and oxidation of the solid oxides has received a great deal of attention. However, knowledge of the kinetics of similar reactions in the liquid state is very meager. Dancy 1 studied the kinetics of reduction of molten iron oxide by carbon in pig iron and found that the reaction is very fast. It was concluded from the results that the reduction of molten ferrous oxide is a first-order reaction up to 80 pct reduction, while

Jan 1, 1964

By D. Kuhlmann-Wilsdorf

A new theory of work hardening is developed which rests on only a few simple principles and is applicable to a wide variety of materials and dislocation structures. It explains, qualitatively, the general characteristics of the three-stage shear stress-shear strain curve of fcc metals, as well as the most important features connected with easy glide. The value of, the work-hardening coefficient in stage 11, is derived quantitatively, from first principles, and is shown to be insensitive to many changes in detailed dislocation behavior. The low rate at which energy is stored during mechanical working in stage 11, the dependence of slip line length on stress, and the so-called Cottrell-Stokes law are explained. Although the theory is primarily developed for fcc metals and alloys, it is largely applicable also to some other materiuls, and in particular apparently to poly crystalline simple steels in theh linear range of hardening. FOR pure fcc metals and alloys, after many different pretreatments and under a great variety of testing conditions, the well-known three-stage work-hardening curve is commonly observed. Moreover, the work-hardening coefficient in stage 11, 011, bears an almost constant relationship to G, the modulus of rigidity, such that K = G/Brr" = 300, within a factor of about 2 either way. The very fact that the three-stage curve and the value of K are so very persistent, can hardly be understood except on the assumption that some quite simple phenomena are responsible. In this light all available theories of work hardening must be judged unsatisfactory: Each of them is based on some quite specific dislocation model, while it is known that metals with similar values of K may have widely different dislocation structures, for example, dislocation tangles in the case of pure fcc metals, and piled-up groups of dislocations in a-brasstype alloys. Thus, while a particular theory might conceivably represent a special case with a reasonable degree of accuracy, it cannot possibly have illuminated the underlying principle. Another severe criticism applying to the presently most widely discussed theories is that they employ empirical or even quite unexplained parameters in order to arrive at a numerical value of K. This indicates that some vital aspect of the work-hardening process has remained unexplained. In the present paper, a new theory of work-hardening is developed which does not suffer from the above shortcomings. It is derived from first principles, and is founded on the realization that the underlying causes for the three-stage work-harden- ing curve and for the persistence of the numerical value of O,, must be few and simple. As a first step it is shown herein that the experimental oklservations on "easy glide" can be explained on the assumption that in this stage dislocations multiply, beginning in a number of restricted area:;, and from there penetrate into crystal regions still substantially free of glide dislocations until a quasi-uniform dislocation distribution has been established. During "easy glide", the resistance to the movement of the foremost dislocations, advancing into still largely a dislocation-free regions, is believed to control the flow stress. This resistance is determined by various factors, among them the reaction of the dislocations against bowing-out into loops, which is due to their line tension. Without such bowing-out no dislocation multiplication would occur, but the corresponding contribution to the flow stress stays practically constant all through stage I. According to the present theory, stage TI begins as soon as there are no more areas left into which newly formed dislocations have not yet penetrated, i.e., as soon :is a quasi-uniform dislocation density has been attaned. Regardless of how, in detail, the dislocations should happen to be arranged at the end of "easy glide", whether in pileups or tangles, on one glide system or on several, the stress necessary to overcome the line tension of the segments must now increase, because the dislocation density increiises while the average free dislocation length decreases. It is argued that all other contributions to the flow stress stay at about the same level as in stage I, and that the said increase in the stress necessary to bow out dislocation segments into loops is responsible for the major part of work hardening in stage 11. Stage TII of the stress-strain curve is explained by largely follouing the ideas of Seeger and his co-workers; however, it is pointed out that the start of stage m may on occasion indicate the onset of "conservative climb" instead of cross slip. Indirect evidence indicates that linear work hardening persists even under the profuse action of cross slip, but at a lower rate. Only when, in addition to cross slip, climb operates extensively, does the work-hardening rat,. drop sharply, ultimately down to zero. BRIEF SURVEY OF EXPERIMENTAL EVIDENCE The stress-strain curve of crystals of many different substances are qualitatively similar. No significant permanent plastic deformation takes place below the so-called "critical resolved shear stress". As the applied stress is raised beyond this level. yielding occurs with little or no work hardening and

Jan 1, 1962

By Richard Moldenke

The paper describes the making of pig iron from the Mayari iron ores of Cuba. The outstanding feature f this pig iron is a considerable content f nickel and chromium. As a marked improvement in the quality of castings has been noted when this iron is used in the foundry mixtures, a series f melting tests f mixtures of great variety of composition was conducted with the idea f getting comparative strengths from which the effect of nickel¬chromium could be seen. These tests, on account of their number, and degree of accuracy desired, were made by the crucible melting method. The paper gives the tables of results, a series f curves showing the inter-relation of the elements involved, and a summary of the conclusions derived. THE presence of nickel-chromium in pig iron made from Cuban ores is so well known that the word "Mayan" is unconsciously associated with it. Since 1904, when exploration of the Mayari deposits of iron ore in northeastern Cuba was undertaken, there has been increasing interest in these ores. The TRANSACTIONS contain numerous references to them. This iron ore, which is shipped to the. United States in the nodulized state, has been thoroughly tested and found very valuable; the deposit covers over 25,000 acres and there is in sight over 500,000,000 tons of ore that, by systematic mining, runs practically constant in composition. With nickel and chromium present, also titanium in sufficient quantities to attract attention, as well as extremely low phosphorus and sulfur contents, the iron founder is naturally interested in the utilization of Mayari ore for pig iron for the better grades of finished iron products. The present point of consumption of Mayari ore is at Sparrow's Point, where Mayari pig iron of any desired composition is made. The com-

Jan 9, 1922

By J. Ruzicka

IN creep testing, material is subjected to a constant load, preferably at a constant temperature, and its rate of deformation is measured. The method of loading can be of various types but in this paper only creep testing under tensile load will be considered. The ordinary tensile test is essentially a comparison test in conditions that frequently bear little or no relation to those under which the test material is to be used in service. The purpose of creep tests is to measure the strength of the test material at slow rates of deformation that more nearly approach the rates realized in service. One purpose of this paper is to illustrate that the creep test, in addi-tion to its value as a service test, is superior to the ordinary tensile test as a sensitive tool for the comparison of certain metals in investigative testing. The other purpose is to describe equipment having distinctive features of design that make it especially suitable for such tests. Representative data obtained with this equipment on a group of rolled zinc-base materials are given. These data are compared with those from practical comparison tests of the creep type on weatherstrip fabri-cated from the same group of materials. The comparison illustrates the value of the fast creep test and of the equipment.

Jan 1, 1937

By J. T. Cherry

A fundamental goal of the Plowshare Program is to predict crater dimensions when an explosive of known yield is buried at a given depth in a given medium. In this paper a technique is presented that seems to calculate adequately, from first principles, the mound and cavity growth that occur during nuclear and high-explosive cratering events. The technique features a standard, numerical approach to high- intensity stress-wave propagation coupled with a unique model of material behavior in brittle failure. A schematic of stress-wave propagation is presented in Fig. 1. The equation of motion provides a functional relation between the applied stress field and the resulting acceleration of each point in the medium. Accelerations, when allowed to act over a small time increment [A]t, produce new velocities, velocities produce displacements, displacements produce strains, and strains produce a new stress field. Time is incremented by [A]t, and the cycle is repeated. The time increment [A]t is determined by an independent stability condition which requires the increment to be smaller than the time necessary far a compressional wave to travel across the smallest zone. We assume that failure occurs in a brittle material when either the tensile strength or the maximum allowable strain energy of distortion is exceeded. When either of these two conditions is violated, the code uses the cracked equation of state to determine the stress. A preshot testing program is used to determine the consolidated and cracked equations of state. In situ properties to be determined by field logging are density and elastic velocity (compressional and shear ve-

Jan 1, 1967

By C. M. Loeb, A. M. Gaudin, J. H. Brown

THE object of most size reduction operations in the mineral industry is to liberate the grains of valuable minerals in the ore from those of the gangue. This is usually accomplished by crushing and grinding the entire mass of ore until there is only a small probability that any single particle contains more than one mineral. During this size reduction only limited control exists over size or composition of the particles exposed to the breaking action, and there is no control over the paths followed by cracks generated during the operation. This lack of control usually results in overgrinding and in production of large quantities of very fine material. The first detriment, overgrinding, is costly in itself, but when combined with the second factor it is doubly so. Not only is the fracture of a free particle unnecessary-the fracture of these particles may also make subsequent separation operations difficult, inefficient, and wasteful. It has been pointed out' that if the object of size reduction is to liberate the valuable mineral component of the ore then, ideally, fracture should follow intergranular paths to the exclusion of trans- granular ones. This would result in liberation of the valuable minerals with as little size reduction as possible. This ideal comminution operation is referred to as intergranular comminution, and it was the object of the investigation to determine the extent to which it could be developed by heat treatments.

Jan 4, 1958

By Samuel Hoyt

This paper gives a short account of plastic deformation as observed in single crystals of zinc, zinc having been selected for the experiments described herein because the phenomena are comparatively so simple and can be studied throughout such a wide range. It is hoped that the paper will serve to show the type of information which studies of single crystals afford and will contribute toward the solution of the general problem of metallic behavior. PRODUCTION OF ZINC SINGLE CRYSTALS The method of Czochralski,1 as modified by vow Gomperz,l was used to produce the crystals studied. The equipment is shown in Fig. 1. Molten zinc is held in a crucible at a temperature which is not far above its melting point, as measured by a pyrometer. A lava disc floats on the melt, and is provided with a central hole about 1 min. in diameter. A glass tube, drawn into a capillary at the lower end, is suspended from a string which is wound up by an electric drive at the speed desired. At the start, the glass capillary is let down into the melt and the hoist is started. The capillary brings up a small quantity of molten metal with it to a point just above the lava disc. At this point, a jet of hydrogen cools it and causes it to crystallize, with the result that a -small crystal forms. As the hoisting is continued, more molten metal is drawn up, in turn to be solidified by the jet of hydrogen. This additional metal continues the growth of the crystal already formed, and a long, cylindrical crystal results. The speed of hoisting used was generally between 0.1 and 0.5 mm. per sec., and the crystals were from 4 to 6 in. long and about 1 mm. in diameter. By varying the conditions, crystals of quite different orientations were obtained and were used in the study of the phenomena to be described.

Jan 1, 1927

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 Robert D. Thomson

LISTED among strategic and critical minerals for stockpiling, mica is an important raw material in electronic and electrical equipment industries. Each year large quantities are consumed in the manufacture of television and radio tubes, radar sets, generators, transformers, electric toasters, and irons. Crude mica, which comes from the mine in crystals or in rough books of various shapes and sizes, is known as run-of-mine or book mica. Structural imperfections, impurities, rough edges, and defective laminae are removed by cobbing, rifting, and trimming to produce a marketable block mica or film mica.' After the rough books have been hand-cobbed to remove adhering rock, dirt, and crushed or defective mica they are rifted, or split. In the U.S. a straight-bladed knife is generally used for rifting. Products of this operation are classed broadly as untrimmed sheet mica and scrap. Sheet mica is any relatively flat piece sufficiently free from physical defects to be cut or stamped into specified shapes for industrial use. Sheet mica is classed as block, film, and splittings. Block mica is not less than 0.007 in. thick with a minimum usable area of 1 sq in. Film mica is split from the better qualities of block mica to groups of specified thickness ranging from 0.0012 to 0.004 in. Splittings are sheets with maximum thickness of 0.0012 in. and minimum usable area of 3/4 sq in. As virtually no mica splittings are produced in the U.S., they will not be discussed in this report. Small, low quality block is subdivided as punch and washer. Punch mica is thumb-trimmed material large enough to yield a circular disk of at least 11/2 in. diam for stained quality mica and 1 1/4 to 2 in. for clear quality. Poorer lots, often referred to as washer mica, are also included in the general term punch mica. Trimming, the next step in processing sheet mica, removes broken and ragged edges, loose scales, and other major imperfections. Trimming may be done with a knife, sickle, shears, or fingers. In the U.S. it is usually done with a 3-in. linoleum knife to obtain a bevel-edged cut. If ragged edges are broken off with the thumb and fingers, the mica is called thumb-trimmed. Full-trimmed is rifted mica trimmed on all sides with all cracks, reeves, and

Jan 1, 1957

By Howard N. Hall

The compressibility of reservoir rock is a factor which is generally neglected in reservoir engineering calculations. This is due in part to the fact that there is little published information on rock compressibility values for limestones and sandstones. Omission of rock compressibility is undoubtedly justified in calculations for saturated reservoirs; however, in under-saturated reservoirs,* expansion of the rock accompanying decline in the reservoir pressure may be of such magnitude as to affect materially the prediction of reservoir performance. The effect of rock compressibility will be of most importance in: (1) calculation of oil in place by pressure decline data in undersaturated volumetric reservoirs when the limits of the field are unknown or indefinite, and (2) studies of natural water drive performance. To estimate its importance in such cases, a series of laboratory tests were made to obtain usable values for reservoir rock compressibility. The total, or effective, compressibility of any reservoir rock is a result of two separate factors, namely, expansion of the individual rock grains, as the surrounding fluid pressure de-

Jan 1, 1953