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By J. A. Musselman, P. F. Gnirk

A study was made of indexed penetrations by a single dull bit tooth under statically applied loads into rock subjected to confining pressures from atmospheric to 5,000 p.si and atmospheric pore pressure. Experimental results obtained with a 45" wedge tooth over the above range of pressures are presented for two limestones and a sandstone, a variely of indexing distances and two degrees of tooth dullness. The optimum distance between successive bit-tooth penetrations required for maximum rock damage and chip formation decreases substantially with increa.sing confining pressure above the brittle-to-ductile transition pressure of a particular rock. However, the distance remains approximately constant for a variation in confining pressure below the transition pressure. At a given confining pressure, the bit-tooth force required lor chip formation is constant for indexing distances greater than optimum, but generally decreases linearly with decreasing indexing distance for distances less than optimum. The chip-formation force data obtained at confining pressures for which the chip-generation mechanism is macroscopic-ally of a pseudoplastic nature compare favorably with previous theoretical results for indexed dull hit-tooth penetrntion into an idealized, rigid, perfectly plastic rock. INTRODUCTION To study the cutting action of a roller-cone bit, the interaction of a penetrating bit tooth with craters formed in a rock surfacc by the passage of previous bit teeth must be considered. Current knowledge of the basic mechanics of bit tooth-rock intcract:on under simulated borehole environmental conditions has been extensively reviewed.',' Particularly of current interest are the effects of bit-tooth shape, distance between successive penetrations and differential pressure at the rock surface on the extent of the interaction. Pertinent to this paper are results of an experimental investigationb f the interaction between successive penetrations by sharp, wedge-shaped bit teeth. It was demonstrated that both bit-tooth angle and differential pressure influence the extent of rock damage between successive bit-tooth penetrations. Specifically, the optimum or minimum distance between successive penetrations required for maximum interact'on or chip generation tends to decrease with decreasing bit-tooth angle and increasing differential pressure. In addition, at differential pressures on the order of 2,000 psi for four va- rieties of limestones and sandstones, the macroscopic mechanism of chip formation exhibits a transition from brittle to ductile. In this paper, experimental consideration is given to successive or indexed penetrat ons by wedge-shaped bit teeth. Since pore pressure in a rock sample is maintained at atmospheric pressure, the differential pressure at the fluid-rock interface is equal to the confining pressure. The degrees of bit-tooth dullness include teeth with flat and round apexes (Fig. 1). Of primary concern in this paper are the bit-tooth forces required for chip formation, the macroscopic mechanism of chip formation and the minimum distance between successive penetrations, i.e., optimum indexing distance required for maximum rock damage, as functions of differential pressure. Of further interest is a comparison of actual bit-tooth chip formation forces at elevated differential pressures with calculated forces from previous theoretical results4 for indexed dull bit tooth penetration into a rigid-plastic rock. EXPERIMENTAL APPARATUS AND PROCEDURE The experimental apparatus consists of a pressure vessel equipped with a piston through the side of the vessel (Fig. 2). A single bit tooth inserted in the lower end of the piston is forced at a desired rate into the rock when the ram pressure chamber is pressurized. Electrical instrumentation incorporated into the apparatus yields a graphical plot of force on the piston as a function of bit-tooth penetration or displacement into the rock. Since the piston and ram assembly are in force equilibrium for a constant confining pressure in the main vessel, the fluid volume in the vessel remains constant during bit-tooth penetration. Hence, the force resisting penetration of the tooth is independent of the force exerted on either end of the as-

By A. T. Corey, J. H. Henderson, M. R. J. Wyllie, C. H. Rathjens

The results of three-phase relative permeability tests on nine water-wet consolidated Berea sandstone samples are presented as composite ternary diagranls showing isoperms of oil, water and gas. Capillary pressure control was exercised over the flow of gas and oil in the presence of water. The water saturations ranged from 17 to 71 per cent pore volume. A method of calculating both the oil and water permeabilities of a three-phase system from the easily measured gas relative permeability is presented. EXPERIMENTAL PROCEDURE AND RESULTS A renewed interest has been shown in three-phase relative permeability as a result of recent developments involving underground combustion processes, steam injection, and other multiphase displacement processes. The experiments and results described here involved simultaneous flow of oil and gas in consolidated Berea sand with brine present as the wetting phase. Gas and oil relative permeabilities were measured on nine cores with CaC12 brine present as the wetting phase in saturations ranging from 17 to 71 per cent. The average residual liquid saturation of the cores was approximately 20 per cent. In order to make certain that brine was the wetting phase, the test cores were saturated with brine before contact with hydrocarbons. As an added precaution to avoid having oil displace brine from the wetting position as a result of changing wettability, each core was only used twice, i.e., first with a fixed percentage of brine and then for a gas-oil permeability determination with no brine present. The results, therefore, are presented as composite ternary diagrams representing the flow tests on nine individual cores having very similar properties. All tests were made using a modification of the capillary pressure techniquc described elsewhere. The effective oil permeability was measured before gas was introduced using a very small pressure gradient (a few centimeters of oil). This determination was made without selectively wet barriers in contact with the core. The cores were then placed between capillary barriers and gas-oil relative permeability curves obtained. The capillary barriers had been made water repellent with a silicone treatment. In determining gas-oil-water relative permeability in this fashion, control was exercised over the capillary pressure existing between the gas and oil. No control was exercised over the pressure difference existing between the oil and water. Athough an equal pressure gradient was applied to the gas and the oil phases, this pressure gradient does not exist in the water phase. Since the pressure gradient across the core was always much less than the displacement pressure of the fully saturated core, the pressure gradient can have caused only a very slight distortion of the oil-water interfaces. This slight distortion of the oil-water interfaces had a negligible effect on the validity of the oil permeabilities measured. The oil permeability, measured in the presence of water but with no gas present, was in every case equal. within experimental error, to the gas permeability of the gas-oil system when the oil saturation was the same as that of the water. Gas and oil relative permeabilities were plotted as a function of total liquid saturation. It was found that the gas relative permeability curves obtained on cores with brine present were identical with those obtained on the same cores with no brine present. The denominator for calculating oil relative permeabilities was the permeability found by extrapolation to infinite mean pressure (A la Klinken-berg). Fig. 1 illustrates gas-oil relative permeability results obtained on a typical core. The solid permeability curves represent the experimental data. The dashed oil relative permeability curve was calculated using the relationship;

Jan 1, 1957

By H. F. Yancey, M. R. Geer, C. L. Allyn, R. H. Eckhouse

Four coals were treated in the Humphreys spiral concentrator, and the products were examined by float-and-sink and screen-sizing tests to determine fundamental performance characteristics. The efficiency of the separation between coal and impurity was shown to be influenced greatly by particle size. FOUR coals exhibiting different washability characteristics were washed in the Humphreys spiral concentrator and the products examined by float-and-sink and screen-sizing tests to determine the mechanics of the separation between coal and impurity. With one coal, each 1/2-in. increment of the full width of the stream in the spiral was examined separately to determine where each size and specific-gravity fraction of the feed was stratified. The basic performance characteristics of the spiral were found to be the same for all of these coals. The coarsest fraction of heavy impurity stratified so far out in the stream that it could not be removed through the refuse ports and thus either entered a middling product or contaminated the washed coal in the case of a two-product separation. Impurity particles finer than about 100-mesh also were carried out in the main body of the stream and therefore were not removed in the refuse product. Little loss of clean coal in the refuse occurred in sizes coarser than 28-mesh or finer than 100-mesh, but considerable coal of intermediate size stratified in the stream that was drawn off through the refuse ports. Because of this modifying influence of particle size, the spiral is unable to make an efficient two-product separation between coal and impurity without some retreatment. Recirculation of a middling product through the same spiral as a means of obtaining more efficient operation was not attempted in this investigation. The size and specific-gravity composition of the middling product are, however, such as to render it amenable to simple hydraulic classification for recovery of coal. Retreatment of a middling product would improve the efficiency of the spiral, but even when making a substantial amount of middling, considerable clean coal enters the refuse product. Consequently, retreatment of a combined refuse-middling product would appear to offer greater promise for providing maximum efficiency. Because of the sizing characteristics of the spiral, a classified feed can be treated with higher efficiency than is possible on a natural raw coal. For this reason, semiclassified feeds, such as silt-bank or classifier-underflow materials, can doubtless be treated with higher efficiencies than those shown for raw coals in this report. Performance is, of course, only one of many factors that enter into the choice of cleaning equipment. The fact that the one company now using the spiral for cleaning coal has built a second spiral plant is ample evidence that the inherently low efficiency of this unit may be overshadowed by the low operating costs afforded by its extreme simplicity. Introduction A number of factors enter into the selection of coal-cleaning equipment, and most of them bear directly on the final cost of prepared coal. One of these factors is performance of the cleaning unit in terms of the efficiency of the separation it effects between clean coal and refuse. The importance of performance in the selection of a coal-cleaning unit varies with the difficulty of the cleaning problem. Obviously, if the character of the coal is such that only certain types of cleaning units are capable of yielding a clean product meeting market requirements, performance is of prime importance. If, on the other hand, the cleaning problem is so simple that any type of cleaner will provide coal of suitable quality, performance is important only insofar as it affects costs by determining the amount of salable coal lost in the washery refuse. With the objective of providing the coal industry with information that is helpful in the selection of

Jan 1, 1951

By R. H. Eckhouse, M. R. Geer, H. F. Yancey, C. L. Allyn

Four coals were treated in the Humphreys spiral concentrator, and the products were examined by float-and-sink and screen-sizing tests to determine fundamental performance characteristics. The efficiency of the separation between coal and impurity was shown to be influenced greatly by particle size. FOUR coals exhibiting different washability characteristics were washed in the Humphreys spiral concentrator and the products examined by float-and-sink and screen-sizing tests to determine the mechanics of the separation between coal and impurity. With one coal, each 1/2-in. increment of the full width of the stream in the spiral was examined separately to determine where each size and specific-gravity fraction of the feed was stratified. The basic performance characteristics of the spiral were found to be the same for all of these coals. The coarsest fraction of heavy impurity stratified so far out in the stream that it could not be removed through the refuse ports and thus either entered a middling product or contaminated the washed coal in the case of a two-product separation. Impurity particles finer than about 100-mesh also were carried out in the main body of the stream and therefore were not removed in the refuse product. Little loss of clean coal in the refuse occurred in sizes coarser than 28-mesh or finer than 100-mesh, but considerable coal of intermediate size stratified in the stream that was drawn off through the refuse ports. Because of this modifying influence of particle size, the spiral is unable to make an efficient two-product separation between coal and impurity without some retreatment. Recirculation of a middling product through the same spiral as a means of obtaining more efficient operation was not attempted in this investigation. The size and specific-gravity composition of the middling product are, however, such as to render it amenable to simple hydraulic classification for recovery of coal. Retreatment of a middling product would improve the efficiency of the spiral, but even when making a substantial amount of middling, considerable clean coal enters the refuse product. Consequently, retreatment of a combined refuse-middling product would appear to offer greater promise for providing maximum efficiency. Because of the sizing characteristics of the spiral, a classified feed can be treated with higher efficiency than is possible on a natural raw coal. For this reason, semiclassified feeds, such as silt-bank or classifier-underflow materials, can doubtless be treated with higher efficiencies than those shown for raw coals in this report. Performance is, of course, only one of many factors that enter into the choice of cleaning equipment. The fact that the one company now using the spiral for cleaning coal has built a second spiral plant is ample evidence that the inherently low efficiency of this unit may be overshadowed by the low operating costs afforded by its extreme simplicity. Introduction A number of factors enter into the selection of coal-cleaning equipment, and most of them bear directly on the final cost of prepared coal. One of these factors is performance of the cleaning unit in terms of the efficiency of the separation it effects between clean coal and refuse. The importance of performance in the selection of a coal-cleaning unit varies with the difficulty of the cleaning problem. Obviously, if the character of the coal is such that only certain types of cleaning units are capable of yielding a clean product meeting market requirements, performance is of prime importance. If, on the other hand, the cleaning problem is so simple that any type of cleaner will provide coal of suitable quality, performance is important only insofar as it affects costs by determining the amount of salable coal lost in the washery refuse. With the objective of providing the coal industry with information that is helpful in the selection of

Jan 1, 1951

By P. L. Rittenhouse, M. L. Picklesimer

A rapid and seniquantitative method of determining prefered orientation on large numbers of. Zircaloy-2 specimens was desired. knoop microhardness measurerrzetzls were irvestigated as a solldtion to this pro6lem. The variation of Knoop microhardness measurerlerzts on selected planes as a function of 'irzdenle axis relutilje lo cryslallograplzic or fabrication divectals were used to corzstrrcl a polar coordinate hardness contour map. With use of an empirical relationslip between the single-crystal hardnesses and those of the polycrystalline material conentional pole figures could be constructed which compare favorably also obtained. To determine preferred oriention qualitatively from hardness data requires a minimum of twelve measurements per plane on three, preferattention to grain size, specimen prepartion, and in-rreinetzt, and analjlsis is of the order of- 45 to 60 rrin. THE design of structures from Zr alloys requires consideration of preferred orientation and the resulting anisotropy of mechanical properties. Rapid and semi-quantitative methods of evaluating anisotropy and of determining preferred orientation are needed for quality control and for examining the large number of test specimens required in development programs. The variation of Knoop microhardness with indenter orientation has been studied in single crystals of several hcp metals including titanium.' beryllium,' magneium, and zinc.4 The maximum hardness observed on any crystallographic plane other than the basal plane invariably occurred when the long axis of the Knoop indenter was either parallel or perpendicular to the projection of the [ OOOI.] direction on the plane of examination. When the major slip mode was (0001)(i2i0j the maximum hardness occurred at the parallel positio! but when the operating slip system was {10i0) (i210) the hardness was a maximum perpendicular to the [0001] projection. A minimum hardness was always observed at a rotation of 90 deg from the maximum. It follows that the orientation of the projection of the [0001] can be determined on any non-basal plane by making hardness measurements at a number of indenter orientations. The determination of the orientation of the [0001] projection on two non-parallel, preferably orthogonal, surfaces of the specimen will allow location of the [0001] direction in the specimen. It seems possible that such measurements could be used to examine, at least qualitatively, the preferred orientation existing in polycrystalline hcp materials. An investigation of the microhardness anisotropy in Zircaloy-2 was undertaken to ascertain whether these measurements could be used for this task. EXPERIMENTAL PROCEDURE Single crystals of Zircaloy-2 were grown by an a-8-a annealing sequence using electron-beam heating.= The orientation of the crystals was determined by a conventional back-reflection Laue technique. The crystals were then mounted on a goniometer head and the desired crystallographic faces were milled and chemically polished. Polycrystalline Zircaloy-2 specimens were prepared from fabricated sheets or plates. Inverse pole figures for these materials were obtained using the X-ray diffraction techniaue described by Jetter, McHargue, and illiams.' A Wolpert-Greis Micro-Reflex hardness-testing machine was used to make the Knoop microhardness measurements. The single-crystal and polycrystalline specimens were loaded to 0.5 and 2.0 kg, respectively. Determination of the scatter of hardness numbers as a function of applied load for several indenter orientations on several specimen surfaces showed that the loads selected were the lightest consistent with minimum scatter. Heavier loads did not appreciably decrease the scatter and produced hardness impressions too large to be conveniently measured with the equipment used. Seven crystallographic planes of the single crystals were examined, while six planes of examination were used in studying Zircaloy-2 polycrystals. The specimens were rotated 10 to 15 deg after each measurement and from four to eight impressions were made at each angle of rotation. RESULTS The two angles which were used to relate crystallographic directions and planes in the hcp cell to the planes of examination of the single crystals are shown in Fig. 1. 8 is the angle between the c axis. [0001]. and the normal, N, to the plane of examination. a is the angle between the long diagonal of the Knoop indenter and the projection of the c axis on the plane of examination. For exampIe, if P = 90 deg and a = 0 deg, the plane of examination is of the family

Jan 1, 1967

By J. M. Blank, V. A. Russell

When the nucleation of silicon on a sapphire substrate is accomplished by gradually decreasing the substrate temperature while subjecting it to a constant impingement rate of hydrogen and silicon tetrachloride, the resulting deposit is characterized by widely separated islands of silicon scattered over an "open sea" of sapphire. Analysis shows that nucleation takes place mainly on sites of large adsorption energy, about 85 kcal per mole, and small surface concentration, about 108 cm-2. Crystal growth proceeds rapidly on these nuclei and results in enough depletion of Sicl4 from the ambient gas to suppress further nucleation. The technological importance of single-crystal films on dielectric substrates has prompted considerable work on the deposition of silicon on sapphire. This paper is concerned with the deposition of silicon, by the reduction of silicon tetrachloride with hydrogen, onto heated sapphire substrates. The apparatus consisted of a temperature-controlled container for the silicon tetrachloride along with gas lines and flow meters necessary to convey a hydrogen-silicon tetrachloride mixture to a reaction chamber constructed of quartz tubing. Heat for the substrate was provided by means of an inductively heated graphite susceptor. The observations pertinent to the present discussion were made with an American Optical Co. high-temperature microscope which allowed us to make motion pictures of the deposition process at a magnification of approximately 50 times. Two main categories of experiments were carried out: one on determination of critical condensation temperatures and the other on the deposition of epitaxial silicon films on the sapphire substrates. Critical condensation temperatures were determined in the traditional way by raising the substrate temperature well above that at which condensation could be expected at the impingement rates being studied and then gradually lowering the temperature until the condensation of the first silicon was observed. This was done initially with ellipsometry-type detection but it was soon discovered that the deposits were occurring as widely separated islands and groups of islands scattered over an "open sea" of sapphire. We have called these archipelago formations. They were most easily detected by optical microscopy. Data gathered from experiments of this type have been collected in Table I. Motion pictures of the formation of archipelago patterns show that the nucleation period lasts about 10 sec if the substrate temperature and impingement rate are kept constant. Essentially all of the nuclei are formed in a few seconds and all subsequent silicon deposition merely adds to the size of the established nuclei. After an archipelago formation has matured at a given substrate temperature and impingement rate, it is very difficult to stimulate any further nucleation in the open space between islands. Lowering the substrate temperature will occasionally stimulate nucleation but increasing the impingement rate hardly ever produces any more new nuclei. It should also be emphasized that the nucleation rates appear to be very small, about 104 cm-2 sec-1. They will receive special attention in the analysis section. Another series of experiments was performed employing a systematic variation of substrate temperatures and impingement rates approximating those expected to produce epitaxy. Sapphire substrates with surfaces normal to the 2233 direction were used. In contrast to the procedure that produces archipelago patterns, these films were deposited by raising the substrate temperature to a desired value at which time the silicon tetrachloride and hydrogen flow was begun. Of course, these depositions produced mainly films that were continuous. After removal from the deposition chamber, the substrate and silicon film were examined microscopically to determine the nature of the deposit and by X-ray diffraction to determine the extent to which a single-crystal film had been achieved. Results of these experiments are summarized in Table 11. Of interest for the present analysis is the fact that epitaxy appears to be confined to a fairly narrow temperature range between about 1050" and 1150°C. This also will be discussed in the analysis section. ANALYSIS In this section we shall apply nucleation theory to the data presented above with the objective of testing

Jan 1, 1967

By G. R. Speich

The precipitation of the Feab and Fe,Ti Laves phases (MgZn, type, C14) from Fe-Nb and Fe-Ti solid solutions, respectively, has been studied in the temperature range 500" to 800°C using hardness measurements, light and electron microscopy, and X-ray and electron diffraction. The Fe-Nb alloys contained 0.96, 1.67, and 3.80 pct Nb and the Fe-Ti alloys 3.5, 5.8, and 8.8 pct Ti. In both systems only the equilibrium Laves phase is formed, with nucleation occurring at grain boundaries, at dislocations, and in the matrix. No cellular precipitation or transition phases were observed. The precipitation of the Laves phase in a fine dispersion leads to significant hardening in both systems. The hardness of the aged alloys is proportional to the reciprocal of the square root of the interparticle spacing. The maximum solid solubility of titanium in a! iron is 9.0 pct Ti at 1280°C. THE precipitation of the FezNb and FezTi Laves phases (MgZn2 type, C 14) from Fe-Nb and Fe-Ti solid solutions, respectively, has been investigated as part of a continuing study of the mechanisms of precipitation from ferritic binary iron-base alloys. The iron-rich portions of the Fe-Nb and Fe-Ti phase diagrams are shown in Fig. l(a) and l(b). The Fe-Nb diagram is essentially that given by ansen' with the more recent work of Hume-Rothery and Gibson2 added. Goldschmidt3 indicates that the FezNb Laves phase has a solubility extending from 32 to 55 wt pct Nb. The Fe-Ti diagram is also essentially that reported by Hansen.l The recent results of Nishimura and kamei, Murakami, Kimura, and Nishimura,' indicate that the FezTi Laves phase has a solubility extending from 22.5 to 30.5 wt pct Ti. The L/6 + FezTi eutectic temperature of 1298°C indicated by Kornilov and oriskina' has been adopted. The addition of niobium or titanium to iron lowers the 6 — y transformation temperature and raises the y — a! transformation temperature. This results in a closed y field in the Fe-Ti system, but the lower solubility of niobium in a! (6) iron results in a eutec-toid, 6 — y + FezNb, at 1200°C, and a peritectoid, y + FezNb —-a, at 989°C in the Fe-Nb system. The maximum solubility of niobium is reported to be 4.5 wt pct in 6 iron,' 1.0 wt pct in y iron,7 and 1.8 wt pct in a iron.' Some results from the present work indicate that the maximum solubility in a! iron is actually less than 0.96 wt pct Nb. The maximum solubility of titanium in a! (6) iron is somewhat uncertain since the early work of To faute and Butting-haus indicated a value of 6.0 wt pct while later work of Kornilov and Boriskina6 yielded a value of 14.0 wt pct. The present work indicates that the maximum solubility is actually 9.0 wt pct. In both systems the phase in equilibrium with the iron-base solid solutions is a Laves phase (Mg znztype, C14), FezNb or FezTi. Both of these Laves phases have a wide range of Solubility. The precipitation-hardening behavior of Fe-Nb or Fe-Ti alloys has not been studied extensively. Genders and Harrison' reported that binary Fe-Nb alloys hardened upon aging. Peter and Fisher7 studied the mechanical properties of Fe-Nb and Fe-Ti alloys quenched from different phase fields.

Jan 1, 1962

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 J. Jones-Parra

In previous Technical Notes, W. R. Rose' and W. Purcell have discussed the capillary pressure data presented by Welge.' Welge obtained capillary pressure curves of the imbibition type in which it was necessary to apply to the apparent wetting phase a greater pressure than that of the non-wetting phase to complete the cycle and reduce the non-wetting phase saturation to low values. Rose suggests in his Note that conditions of equilibrium could not have prevailed, since the. non-wetting phase pressure must always be the greater. Pur-cell in his Note, proceeds to postulate a pore system consisting. of a series of "holes in a doughnut," in which he contends that under equilibrium conditions it is necessary to resort to negative capillary pressures before significant wetting phase displacement can take place. There is a remarkable similarity between the shape of the capillary pressure curve calculated by Purcell and those measured by Welge. It is the purpose of this Note to show that, because Purcell neglected to account for the behavior of the residual wetting phase saturation, his system was not in equilibrium during imbibition; and, furthermore, that if his system had been in equilibrium, negative capillary pressures would not have been possible. In Purcell's pore system, the residual wetting phase will form pendular rings at the interstitial spaces existing somewhere within the system, for example, such as those spaces between "doughnuts" as shown in Fig. 1. The true capillary pressure is that across the pendular ring interface, and for the system to be in equilibrium the pressure drop across all interfaces must be the same, including that across the interface in the tight pores A of diaphragm B (Fig. 1). As the pressure across the cell is reduced, the advancing interface will move into the pore from the diaphragm, but at each pressure, the curvature of the pendular rings must be the same as that of the advancing interface if equilibrium is to prevail. Since equilibrium conditions are the basis for the entire argument, it follows that pendular rings must grow as wetting phase enters the pore, that is, as the pressure across the cell is lowered. In Purcell's calculated curve, the residual wetting phase saturation remains constant as the capillary pressure decreases. Thus, his curve does not represent an equilibrium process.

Jan 1, 1953

The following correspondence relating to a paper bearing the above title, presented by J. F. Wolff, at the New York meeting in February, 1917, and published in the Transactions, Volume LVI, page 142, has passed between the author of the paper, and Mr. Anson G. Betts, and is interesting, although it was received much too late for incorporation in its proper place in Volume LVI. ANSON CT. BETTS, Asheville, N. C.-1. I should like to ask Mr. Wolff if he finds-from analysis of the iron formation and of the iron ore, and from the relative amounts of each in each unit area of the formation, unleached and after leaching, that the iron remains entirely insoluble and the total quantity still remains present; or whether he finds that some of the iron is removed, or possibly even added by deposition from the water passing through the formation. 2. The water that passed into the iron formation had to go somewhere; was it absorbed by underlying formations through hydration, or, after passing through the ore formation, did it come to the surface in springs at a lower elevation, or how did it escape from the ground? 3. I should like to ask Mr. Wolff whether he finds that the iron formation in the sedimentary series does not, come next to the quartzites and generally between the quartzites and slates. J. F. WOLFF, Duluth, Minn.-1. In common with others, you appear to have some hesitancy in accepting the fact of the removal, by solution, of the enormous quantity of silica which has been leached out of portions of the Biwabik iron formation, thus forming orebodies of merchantable iron ore. I believe that even Dr. Waldemar Lindgren once hesitated to accept this fact. However, the evidence is so simple and absolutely conclusive that the fact is established beyond all question. At the contact of orebodies with their rock walls, the bands of iron ore in the orebody can be seen in contact with the corresponding bands of original iron oxide in the rock wall, and the chert layers in the rock wall can be seen to give place to fine granular material (fine silica and iron oxide) and pore space. This is especially noticeable where slumping at the rock walls his not been so great as to displace the layers in the orebody from their contact with their corresponding layers in the rock wall.

Jan 9, 1918

By C. W. Lawr

The ores mined by the Santa Gertrudis Co. at Pachuca, Mexico, arc mainly silver-bearing; they also yield some gold and carry a little copper. Strong cyanide solutions are used to dissolve the silver and gold, and the mechanical loss of cyanide at the tailings filter has been considerable. Prior to the year 1923, the pulp, after agitation, was given a 35 to 37-min. wash with barren solution in a Butters-type leaf filter; the discharged slime cake was repulped and pumped into eight Merrill self-sluicing slime presses in which the slime was given a further wash with barren solution for 25 to 35 min., followed by a 10-min. water wash. At that time the barren solution titrated around 0.350 per cent. free KCN and 0.500 per cent. total KCN. (Aero brand cyanide is used.) It can readily be seen that a 10-min. water wash would leave considerable cyanide in the filter cake, which of course was a total loss. This averaged 0.522 kg. (1.15 Ib.) KCN per ton of solution. As the daily discharge to the dam was 1600 tons' of slime of a 2:1 ratio of liquid to solid, the value of this mechanical loss of cyanide was an important item and it's recovery held alluring possibilities. Principle of Cyanide-recovery Process As it had acquired the patent rights to theLayng (H. R.) and Halvor-sen (A. L.) processes, also those of Mills (L. D.) and Crowe (T. B.) after considerable experimental work in its own laboratory and at Tonopah, Nev., The Merrill Company of San Francisco early in 1923 notified the Mexican Corporation and compania de Santa Gertrudis of its process for the recovery of cyanide from weak wash solutions, or for the transference of cyanide from a foul mill solution to a clean alkaline solution. This method is known as the Mills-Crowe process, the principle of which is as follows: The solution from which the cyanidc is to be removed is made acid by bringing it into contact with sulfur dioxide (SO2). The acidified solution is the; transferred to a closed tank in which air and solution are brought into intimate contact. The air leaving the tank charged with HCN is then passed to another tank in which it is mixed with an alkaline solution,

Jan 1, 1930

By M. T. Martinson, I. W. Nicholson, C. J. Chindgren, F. P. Williams, L. C. Bauerle, S. F. Ravitz

THE vanadiferous shales of southeastern Idaho and southwestern Wyoming constitute the largest known reserve of vanadium in the United States.1 These deposits have never been exploited except for the relatively small amounts of vanadium recovered by the Anaconda Copper Mining Co. in the treatment of phosphate rock from southeastern Idaho. The major domestic source of vanadium has been the sandstone ores of southeastern Utah and southwestern Colorado. Early in World War II, it appeared that these ores could not meet the greatly increased demand for vanadium, so the investigation described in this report was undertaken to develop processes for the recovery of vanadium from the Idaho-Wyoming deposits. The utilization of these deposits became unnecessary, however, because of greatly expanded production from the Utah-Colorado sandstone ores and the continued availability of vanadium from other sources, chiefly Peru. The major use of vanadium is as an alloying agent in the manufacture of high-quality steels. Vanadium constructional steels usually contain 0.05 to 0.20 pct vanadium, which refines the grain and increases the strength, elastic limit, and resistance to shock and fatigue. Vanadium tool steels not used in high-speed work contain 0.10 to 0.60 pct whereas high-speed tool steels contain 1.0 to 4.0 pct. Vanadium compounds are used as catalysts (principally for the oxidation of SO2 to sulphuric acid and of naphthalene to phthalic acid) and in the paint, chemical, ceramic, dye, and printing industries. The selection of the particular ore deposit to be exploited would involve consideration of many factors besides the metallurgical results that might be obtained. Chief among these would be the reserves of ore available, the grade of the ore, and the mining costs. As very little was known about any of these factors, it was necessary to investigate methods of treatment of all the ores under consideration, working with samples obtained in the course of the exploration work, even though they were not positively representative of the whole deposit from which they were taken. Because of wartime conditions prevailing when this investigation was started, first consideration was given to processes that could be put into operation most quickly and would involve minimum use of strategic materials, even though these processes might not be the most economical.

Jan 1, 1947

By George C. Ference

Sulfur is the 13th most common element in the earth's crust, constituting approximately 0.05% of the total. It occurs naturally in its elemental form, as metallic sulfides, nonmetallic sulfates, and as combined or free sulfur in natural gas, crude oil, and coal. COMMERCIAL SOURCES Most of the sulfur that is consumed is converted into sulfuric acid before use; therefore, it is not necessary to recover sulfur solely in its elemental form. Processes for recovery are peculiar- to the types of reserves being processed. The major commercial processes as well as the general geographic locations where the appropriate reserves occur are listed in the following. It should be noted that the sulfur values may be recovered as the primary product, as a coproduct with other materials, or as a byproduct. Elemental Sulfur 1) Frasch mining is used for subterranean deposits of elemental sulfur around the Gulf Coast areas of the United States and Mexico. Generally, but not exclusively, such deposits are located in salt dome structure. 2) Autoclaving, flotation, or solvent extraction of surface deposits of elemental sulfur is practiced throughout the world. 3) Extraction and conversion of hydrogen sulfide from sour natural gas into elemental sulfur is done principally in Canada, France, and the United States. 4) Conversion of metallic sulfides from pyrites into elemental sulfur is done via the Outokumpu process in Finland. 5) Catalytic cracking and hydrocracking of sulfur-bearing crude oils to produce elemental sulfur is done worldwide. Desulfurization of refined petroleum products also yields elemental sulfur. 6) Recovery of elemental sulfur from sulfur-bearing oil sands (Athabasca tar sands) has been initiated in Canada. 7) As of this writing (1970), a plant has been constructed for the thermal decomposition of gypsum to produce elemental sulfur in the United States. Sulfuric Acid Sulfur values in the form of sulfuric acid are recovered via: 1) Recovery from smelter gases throughout the world. 2) Roasting of pyrites throughout the world with iron sinters as a byproduct. 3) Roasting of anhydrite with cement as a coproduct, primarily in Europe. 4) Processes currently are being developed for recovery of sulfuric acid from combustion gases resulting from the burning of high-sulfur-content fuel. Other Sulfur values also are recovered from waste products which normally occur in highly industrialized areas. Some examples are: coke-oven gases, sludge sulfuric acid, and pickling liquors (ferrous sulfate).

Jan 1, 1976

By H. F. Seifert

The classification and preparation of non-ferrous scrap mctals is a subject of interest to every individual and corporation that employs in its processes of manufacture non-ferrous metals and alloys and accurnulates in such manufacture scrap from these materials for disposition in the form of turnings, borings, short ends, punchings, clippings, grindings, washings, etc. All too frequently the disposition of such scrap is left to indivitluals who have no knowledge of the subject either from a metallurgical or a commercial standpoint, or both. Much money is thus lost whicli with a little more intelligent effort might be saved, and in this day of fierce competition and small profits such an opportunity cannot be ignored. The Mineral Resources of the United States for the year 1925, the latest issue available (Part 1, page 221), gives the secondary non-ferrous metals of certain classes recovered in the United States for the year 1924 to 1925 as shown in Table 1. The figures are tabulated simply to give the reader some idea of the scope of the secondary non-ferrous metal industry. Approximately 900,000 tons of an annual value of $244,000,000 were recovered in the year cited. In 1916 (again using thc Mineral Resources of the United States as authority) the tonnage reclaimed was approximately 632,000 tons and the value, because of the high prices for metals prevailing at that time, amounted to $265,000,000. It is not the purpose of this paper to discuss smelting and refining operations or the feasibility of an organization, primarily engaged in some other activity, conducting smelting and refining operations to convert its own non-ferrous scrap metals and alloys. The classification and preparation of these non-ferrous materials is a preliminary step, regardless of what subsequent operations the material may pass through or where these operations may be conducted. For that reason the subject can he readily discussed without any reference to subsequent activities. Space must be provided, with suitable handling facilities, scales and the necessary storage bins where the material may be accumulated. The scope of the activity, the nature of the industry and the tonnage handled will determine, in a large measure, what preparation, if any, it rrlay he desirable to give these scrap materials to put them in the best niarketable condition. By preparation is rneant largely what, for the want of a

By A. R. Elsea, C. C. McBride

HIGH-TEMPERATURE alloys, that is, alloys that are strong at high temperatures, have become increasingly important with the development of modern aircraft engines. Many alloys of this type are available. However, metallurgists do not have a clear understanding of the phases or structures which are responsible for these high-temperature properties. If these basic factors were understood, it might be possible to make better or cheaper alloys for service at high temperatures. For this reason, an investigation of the fundamental factors promoting high-temperature strength in alloys was started at Battelle Memorial Institute. This was to have included a study of the relationship between the structure and properties of cobalt-chromium base alloys of the vitallium type. It soon became clear that the structure of vitallium is quite complex and that the equilibrium diagrams which should explain these structures were unreliable. As a result, the cobalt-chromium binary diagram was determined as the first phase of this investigation1. This diagram is shown in fig. 1. During the study of the cobalt-chromium binary system, it was learned that these alloys may pick up considerable nitrogen when melted and heat treated in air. The extent to which nitrogen affects the various reactions in cobalt-chromium base alloys was not known, but there were indications that this impurity might be responsible for some of the erratic test results obtained for vitallium. Consequently, nitrogen was the first ternary addition studied. Thereafter the work was extended to ternary additions of iron and of nickel. This paper describes the investigation of the effects of nitrogen, iron, and nickel upon the reactions in cobalt-chromium alloys with 80:20 and 68:32 cobalt-chromium ratios. Experimental Work Alloy Preparation: A series of cobalt-chromium base alloys containing various amounts of the third element being studied were made for both the 80:20 and the 68:32 cobalt-chromium ratios. Electrolytic chromium, cobalt, and iron, and reagent-grade nickel powder were used as melting stock. Table I contains the chemical analyses of these materials. The charges were melted in alun-dum thimble crucibles which absorbed chromium oxide and effectively deoxidized the melts. These crucibles were supported by close-fitting graphite sleeves so that if they cracked during melting the metal would not be lost. Carbon increases, during

Jan 1, 1951

By H. F. Seifert

THE classification and preparation of non-ferrous scrap metals is a subject of interest to every individual and corporation that employs in its processes of manufacture non-ferrous metals and alloys and accumulates in such manufacture scrap from these materials for disposition in the form of turnings, borings, short ends, punchings, clippings, grindings, washings, etc. All too frequently the disposition of such scrap is left to individuals who have no knowledge of the subject either from a metallurgical or a commercial standpoint, or both. Much money is thus lost which with a little more intelligent effort might be saved, and in this day of fierce competition and small profits such an opportunity cannot be ignored. The Mineral Resources of the United States for the year 1925, the latest issue available (Part 1, page 221), gives the secondary non-ferrous metals of certain classes recovered in the United States for the year 1924 to 1925 as shown in Table 1. The figures are tabulated simply to give the reader some idea of the scope of the secondary non-ferrous metal industry. Approximately 900,000 tons of an annual value of $244,000,000 were recovered in the year cited. In 1916 (again using the Mineral Resources of the United States as authority) the tonnage reclaimed was approximately 632,000 tons and the value, because of the high prices for metals prevailing at that time, amounted to $265,000,000. It is not the purpose of this paper to discuss smelting and refining operations or the feasibility of an organization, primarily engaged in some other activity, conducting smelting and refining operations to convert its own non-ferrous scrap metals and alloys. The classification and preparation of these non-ferrous materials is a preliminary step, regardless of what subsequent operations the material may pass through or where these operations may be conducted. For that reason the subject can be readily discussed without any reference to subsequent activities. Space must be provided, with suitable handling facilities, scales and the necessary storage bins where the material may be accumulated. The scope of the activity, the nature of the industry and the tonnage handled will determine, in a large measure, what preparation, if any, it may be desirable to give these scrap materials to put them in the best marketable condition. By preparation is meant largely what, for the want of a

Jan 1, 1928

By H. D. Colson, Robert A. Rapp

When a binary alloy is oxidized to form simultaneously an internal oxidation zone and an external scale which grows at a constant rate, the oxidation should reach a condition of steady shale, in which the internal oxidation zone is maintained at a time-independent thickness. Assuming an ideal model for the steady-state oxidation, the diffusion equation is solved for the steudy-state concentration profiles for oxygen and alloying- element in the metal. A theoretical prediction of' the steady-state thickness of the internal oxidation zone is made in terms of the experimental parameters. FOR the oxidation of binary alloys, Rhines, Johnson, and Anderson,1 as well as Mask: have derived equations describing the kinetics for the simultaneous formation of an internal oxidation zone and an external scale which was assumed to mow according to a parabolic rate law. Experimental determinations of internal oxidation zone thicknesses beneath a Cu2O scale for Cu-Be and Cu-A1 alloys3,4 have shown some deviation from Maak's theoretical expressions, because the ideal model assumed for the calculation is not met experimentally. Some pure metals, such as columbium and tantalum oxidize at elevated temperatures and high oxygen pressures to form nonprotec-tive external scales which thicken at a constant rate. If such a base metal is alloyed with a solute element which may form a more stable oxide than the solvent oxide, then internal oxidation of solute may occur beneath the growing external scale. A review of the internal oxidation of alloys has been published recently.5 The purpose of this paper is to analyze theoretically for a binary alloy the kinetics for the simultaneous formation of an internal oxidation zone and an external scale which grows at a constant rate. Consider an alloy A-B in which A is the more-noble solvent and B is the less-noble solute. The solute oxide is assumed to precipitate in internal oxidation as stoichiometric particles of BO, which are assumed to have a negligible solubility product in the A matrix. It is further assumed that the diffusion of oxygen through the zone of internal oxidation is not impeded by previously precipitated BO, particles. The specimen is assumed to be sufficiently thick so that the solute content in the center of the specimen does not change. For consistency: the following notation of Maak2 has been used:

Jan 1, 1967

By C. A. Wert, M. G. Coleman

The Zener relaxation in alloys in the a! solid-solution region of the Cu-Ni-Zn ternary system has bear investigated. Of the binary solid solutions that bound this region, Cu-Zn and Ni-Zn exhibit measurable Zener peaks whereas Cu-Ni does not. At constant atomic percent copper, the Peak height drops uni.forinly from the value in the Cu-ZTL binary to zero in CIA-Ali. The cariation of peak ternperatuve with composition is linear. At constant atomic percent zinc, the peak height in the ternary alloys goes through a large maximum as compared with the binary values. The temperature of these peaks varies smoothly with composition. The half-width of the peaks in the ter nary alloys, however, are much larger than those in the binaries. A large enhancement of the relaxation strength of the Zener relaxation in ternary Au-Ag-Zn alloys as compared to the relaxation strengths in Au-Zn and Ag-Zn binary alloys was observed by Firson and ert.' Since this effect was unexpected, the present study was devised to investigate whether enhancement of the Zener relaxation in ternary alloys is a general feature or is particular to the Au-Ag-Zn system. We have chosen the Cu-Ni-Zn alloy system for this investigation. Measurable Zener relaxations are observed in both the Cu-Zn and the Ni-Zn binary systems, but not in the Cu-Ni binary system. A large solid-solution region extends to large concentrations of zinc, making it possible to vary composition of the alloys over a wide range without crossing phase boundaries. EXPERIMENTAL PROCEDURE Two series of alloys were prepared. the first at constant atomic percent copper, the second at constant atomic percent zinc. The compositions of these alloys are shown by the circles in Fig. 1. The alloys were prepared by melting the individual components, each of which had previously been vacuum-melted, in an evacuated quartz capsule in an induction furnace at 1500 C. The capsules containing the molten alloys were quenched in water to reduce coring. Any individual melt which exceeded 0.001 pct weight loss was discarded. The ingots were swaged to a 50 pct reduction of area and annealed for 1 week in an evacuated quartz capsule to aid homogenization. The alloys were then

Jan 1, 1967

By D. Mizer, J. B. Clark

In a recent investigation of the entire magnesium-yttrium phase diagram, Gibson and Carlsonl report the maximum solid solubility of yttrium in magnesium as 8.0 wt pct Y at 1050°F (565°C). However, independent studies of the precipitation in magnesium-yttrium alloys, 2 conducted prior to the publication of the above phase diagram, indicated a greater solid solubility of yttrium in magnesium. Accordingly, the magnesium-rich region of the diagram was re-investigated to determine more accurately the liqui-dus, solidus, and solvus of the magnesium solid solution in this system. Metallography and thermal analysis were chosen as the best corroboratory methods for accurately determining this region of the diagram. A magnesium-yttrium master alloy was prepared from yttrium of 99.9 pct purity and singly sublimed magnesium of 99.9 pct purity. Subsequently, the twelve magnesium-yttrium alloys shown in Fig. 1 were prepared using standard alloying procedures for magnesium. Metallographic samples of the alloys were heat treated under an SO, atmosphere in an electric furnace capable of control within ±3oF of the desired temperature. Alloy samples for the metallographic determination of the solvus, and for the precipitation studies were solution treated at 1000° F for 16 hr. Subsequent aging times for the solvus determination varied from a minimum of 6 hr for the higher temperatures up to 816 hr for lower temperatures. Periods of 30 min at temperature were used to generate liquation for the metallographic placement of the solidus and eutectic horizontal. The liquidus and the eutectic horizontal were determined by thermal analysis. Simple time-temper- ature heating and cooling curves were obtained from 10-g alloy samples heated and cooled in a well-insulated electric furnace. An Iron-Constantan thermocouple was placed in direct contact with the sample. The thermocouple did not contaminate the alloy sample since metallographic examination showed that the alloy melt did not wet or attack the thermocouple. The heating and cooling rates were approximately 5 to 8OF per min. The standard metallographic procedures for magnesium were used in polishing and etching the magnesium-yttrium alloys studied. Glycol etchant* was etchant was used to reveal precipitate in the solvus determination. The redetermined magnesium-rich region of the magnesium-yttrium diagram is shown in Fig. 1. The

Jan 1, 1962