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By Frank T. Sisco

DURING the past year the iron and steel industry of the world as a whole operated on a satisfactory basis. No discoveries nor new processes of outstanding importance were announced either here or abroad, although rumors of such were persistent. In general, the efforts of operating and research men in the iron and steel industry seemed to be confined to improving quality and reducing cost, not a new aim, for the same efforts have been noted in nearly all of the annual reviews of the industry for at least fifty years. Most published papers on blast furnace or steel-making practice were of minor importance, at least when judged by the criterion of radical change in process or product. If the number of reports in the technical journals, or articles in the trade press, is used as a basis for comparison, continuous-mill sheet is still the most important single product of the industry; papers were published detailing the results of the investigation of various phases of the

Jan 1, 1938

By J. L. Huitt, D. K. Lowe

This laboratory flow study covers propping agent transporl in horizontal fractures as influenced by the characteristics of the propping particles, fluid and fracture. Correlations are presented for the transport of particles, deposition and fingering through dunes. For particles moving individually, the article velocity in some cases may be low compared to the hulk average fluid velocity; in other cases, the particle velocity may exceed the bulk average fluid velocity. At high propping agent concentration or low fluid velocity, the likelihood of particle deposition and dune formation increases. Fingering and channeling accompany dune formation. Dune formation can be limited to the outer region of tile fracture by adjustment of pump rate, fluid viscosity and particle concentration. A method is presented by which pump rate and fluid vircosity may he selected to control dune formation for given propping agent concentrations. INTRODUCTION The area and flow capacity of a fracture predominantly control the stimulation derived from hydraulic fracturing. Generation of fracture area exposes the rock matrix to a flow channel; the flow capacity of the fracture controls the flow through the channel to the wellbore under a given pressure gradient. This paper pertains to an important factor that affects the flow capacity of a fracture: the transport of the propping particles in the fracturing during the hydraulic fracturing treatment. With a better understanding of particle transport, fracturing treatments may be designed to obtain more effective distribution of the propping agent. RELATED STUDIES In recent years, the approach to obtaining high fracture flow capacity has been partial monolayer propping. Three papers1-3 have dealt with various facets of this concept. However, in some papers dealing specifically with particle transport, the results generally indicate that packing the propping particles within a fracture is inevitable. In early work&apos; with a sand slurry flowing in a pie-shaped flow cell, qualitative results showed that particle deposition in a fracture during transport should be expected. In other studies"" correlations based on slurry flow in vertical linear flow cells showed particle deposition was primarily a function of fluid velocity. In a recent paper the rate of sand advance (movement of dunes) in a horizontal linear flow cell was discussed. Subsequently, a method was given for designing fracturing treatments, based on the extent of sand advance during a treatment. In this work, particles whose diameter was small relative to the fracture width (i.e., dl W< 0.2) were primarily considered. The particle transport approaches that of sand transport in a stream bed. The industry trend, however, has been to use larger size propping agents. That is, particles with diameters approaching fracture widths predicted by Perkins and Kern.&apos;&apos; This trend has led to generally better fracturing treatments with particle relative sizes in the range 0.2 <d/W < 1.0. In all of the particle transport studies previously cited, the fluid characteristics were discussed. However, little or no attention was given to the parzicle characteristics. In this study the particles. as well as the fluid and fracture, are considered. VARIABLES AFFECTING PARTICLE TRANSPORT In the exploratory work to set LIP a program for this study, it was noted that particles within a batch moved at different velocities in a horizontal linear flow cell. In some cases the particles moved independently. In others there was particle interference. Also, particle deposition and fluid fingering occurred in some cases (Fig. 1). As a result of observing the easily distinguishab&apos;le types of particle movement, the particle variables as well as the fluid variables were included. In addition, the fracture width was included because the fluid velocity profile surely must affect the movement of the larger particles differently than that of smaller particles. Particle variables were density, diameter (based on a sphere of equal volumetric displacement), long and short dimensions, drag coefficient and velocity. Fluid variables were density, viscosity, yield shear strength and velocity. Fracture variables were the width and the angle between the plane of flow and a horizontal plane. Two factors which may prove to be important were omitted because of the complexity resulting from the parameters cited above. These are the fracture-surface roughness and gross irregularities that cause changes in the direction of flow. EXPERIMENTAL EQUIPMENT AND PROCEDURE A linear parallel-plate flow cell (Fig. 2) was used in the study. Lucite plates 1 in. thick formed the test section and permitted a viewing section 11 ft long and 10 in. wide. Spacing between the plates was adjusted with shims to give fracture widths 1/36 to 1/2 in. The model could be tilted to an angle of 45" with the horizonltal plane. Fluid flow was maintained with a Moyno positive displacement pump. Single particles were placed in the flow stream with a particle injector. A .4 - in. diameter plunger moving at a constant rate in a

Jan 1, 1967

By Donald L. Johnson

REVIEWS on the applications of optical ellipsometry to the study of polycrystalline metal surfaces and oxidation-corrosion processes have been presented by Kruger and Hayfield, and white.&apos; In view of the ability of this method to measure differences in film thicknesses to below 10A, ellipsometry was used to study nitrogen chromium surface reactions during the early stages of growth. Chromium specimens in the form of a vapor-deposited film on glass substrate were exposed to purified nitrogen for selected time increments at 700°F. This temperature was selected because it gave the best combination of exposure time and thickness change. Ellipsometer readings were taken immediately after exposure to determine polarizer and analyzer angles using monochromatic light at 5000A.2 After each set of readings was obtained, the specimens were exposed for an additional increment of time in nitrogen and a new set of readings taken. Film thickness was computed from LUCy&apos;s3 equation for nonabsorbing thin films. In Lucy&apos;s derivation, two equations for computing thickness were obtained. Peterson and Bashara4 have discussed the validity for using one of these equations when an independent value of the refractive index is used. The film was assumed to be Cr2N (Ref. 5) and was determined to be optically isotropic. Optical isotropy was determined by rotating the films about the surface normal and noting that the azimuth and phase difference did not change. Since Cr2N is reported to be hexagonal, it is assumed that optical isotropy results from randomly oriented grains of very small size. The thickness was computed using refractive indexes varying from 1.6 to 2.0. The maximum variation in computed thickness over this range for a given exposure was 20 pct. The data reported are based on a refractive index of 1.8. Reference readings on the metal surface were taken just prior to nitrogen exposure. No attempt was made to deoxidize or denitride the metal surface after vapor deposition, although specimens were observed to gain approximately 2A per day in air at room temperature. Twelve experimental exposures were made on a single sample over a total accumulative time of 132 min. Additional experiments over longer time intervals were made to determine the effect of heat up and cool down during and after exposure. As a result of these experiments, the thickness computed for each exposure was increased by 4A. Time profiles based on the linear law are similar to the oxidation profiles for many metals.&apos; The rate of accumulation of the nitride film is rapid at first and slows down as the film thickness increases. The parabolic law x2 =k1t +k2 [11 gives a straight line in Fig. 1; therefore, it is concluded that the kinetic behavior is parabolic. Sey-bolt and Haman5 reported similar results for CrlN on chromium at 1000°C although the order of the thickness was much greater (10-3 cm). Analysis of thickness data based on other values of refractive index shows that the curves are shifted vertically but retain the same shape. According to Mott,7 it is expected that for thin films k2 is zero in Eq. [I]. Since the plot in Fig. 1 is linear through the origin, k2 is zero and the parabolic nature of the film growth is further indicated. The parabolic rate constant, calculated from the slope in Fig. 1, is 4.4 x 10-16 sq cm per sec. The corresponding work (+) required to bring an electron from the metal into the oxide is estimated to be 1.5 ev.7 The author thanks professor N. M. Bashara and D. W. Peterson, Electrical Materials Laboratory, University of Nebraska, for making the ellipsometer available and providing technical assistance. The Electrical Materials Laboratory is supported by the office of Naval Research, NONR 3718 (01). This work was partially supported by the Engineering Experiment Station and the Mechanical Engineering Department, University of Nebraska.

Jan 1, 1967

THE National Coal Association held its annual meeting at Cleveland on Nov. 14-16, 1928, having changed the time from the spring to the autumn to avoid conflict with the great number of meetings ordinarily held in the spring. Institute members were \\yell to the fore in its activities, the president, E. C. Mahan (who was reelected for another term!, C. E. Bockus, treasurer, and the secretary, H. L. Gancly, being A. I. M. E. members, as are many of the directors. At the first session, our past president, S. A. Taylor, presented a 1;aper which is reprinted in part herewith. At the Thurs- day session W. D. Brennan presided, Walter Barllum led the discussion on membership, and Otis Mouser led the discussion on taxation. In the afternoon, J. P. Williams, Jr., led the discussion on research. Rembrandt Peale presided at the annual dinner in the evening. At the concluding session on Friday resolutions were adopted, among them one in which the Association "reaffirms its attitude toward proposed Federal legislation affecting the bituminous coal industry by saying that it opposes legislation which would seek to single out this industry for regulatory action. This particularly applies to such bills as S4490."

Jan 1, 1928

By Thomas M. Drown

Remarkable as have been the direct results of Danks&apos;s puddler, there are some indirect and incidental results, which are well worthy of study for their intrinsic value and suggestiveness. The success of Danks&apos;s machine is due mainly to the nature of the lining and the manner in which it is attached to the walls of the revolving chamber. Herein lies Danks&apos;s merit and good fortune. Given such a lining, and the success of the machine, as far as puddling iron is concerned, could easily be predicted. Other important results have, however, been obtained with this machine, which, though clearly explicable, were, nevertheless, unanticipated. These are the increased yield of bar-iron over the pig-iron charged, and the elimination of phosphorus, which, though not absolutely complete, is yet more decided than in the case of hand-puddling. As regards the increased yield, this is merely what we have a right to expect if we consider the puddling process to consist in the oxida tion of the carbon and silicon of the pig by the oxygen of the oxide of iron. That this result is attained, nearly to the extent that the theory requires, in Danks&apos;s puddler, and has never been more than partially attained by the most careful experiments in band-puddling, points clearly to the fact that the contact of the molten pig-iron with the oxide of iron is much more intimate and complete in the one instance than in the other. The action of puddling in Danks&apos;s machine may be considered to be twofold: first, the removal of the carbon, silicon, and phospho rus of the pig, which is the primary object, and, second, the produc tion of wrought iron direct from the ore, which is entirely an inci dental result. Intelligent metallurgists were not long in recognizing in this latter result a fact of deeper import and greater value than the attainment of a perfect puddling process. A new method

By Thomas M. Dr. Drown

REMARKABLE as have been the direct results of Danks&apos;s puddler, there are some indirect and incidental results, which are well worthy of study for their intrinsic value and suggestiveness. The success of Danks&apos;s machine is due mainly to the nature of the lining and the manner in which it is attached to the walls of the revolving chamber. Herein lies Danks&apos;s merit and good fortune. Given such a lining, and the success of the machine, as far as puddling iron is concerned, could easily be predicted. Other important results have, however, been obtained with this machine, which, though clearly explicable, were, nevertheless, unanticipated. These are the increased yield of bar-iron over the pig-iron charged, and the elimination of phosphorus, which, though not absolutely complete, is yet more decided than in the case of hand-puddling. As regards the increased yield, this is merely what we have a right to expect if we consider the puddling process to consist in the oxidation of the carbon and silicon of the pig by the oxygen of the oxide of iron. That this result is attained, nearly to the extent that the theory requires, in Danks&apos;s puddler, and has never been more than partially attained by the most careful experiments in hand-puddling, points clearly to the fact that the contact of the molten pig-iron with the oxide of iron is much more intimate and complete in the one instance than in the other. The action of puddling in Danks&apos;s machine may be considered to be twofold first, the removal of the carbon, silicon, and phosphorus of the pig, which is the primary object, and, second, the production of wrought iron direct from the ore, which is entirely an incidental result. Intelligent metallurgists were not long in recognizing in this latter result a fact of deeper import and greater value than the attainment of a perfect puddling process. A new method

Jan 1, 1874

By Warden A. Moller

(Pittsburg Meeting, March, 1910.) THE Fushun coal-field, now being opened up by the South Manchurian Railway Co., is connected with the main line by a branch, 30 miles long, from Sui Chia Tun, 10 miles south of Mukden, the capital of Manchuria. The coal-field, which lies on the southern bank of the Hun river, 25 miles east of Mukden, consists of a long narrow valley,. running east and west between hills composed of granitic and volcanic rocks. At the foot of the northern hills, the Hun river flows westward towards the Liao river, which drains the greater part of South Manchuria. At the foot of the southern hills, resting immediately upon volcanic rocks, and overlain by 20 ft. of alluvial, is a thick layer of Tertiary shales, carrying near the base two coal-seams. In many places the lower of these two seams is in immediate contact with volcanic lauds and basalts, the flows of which were evidently both prior and subsequent to the formation of the coal-seams. This contact has practically destroyed the lower seam for commercial purposes. The value of the field lies in the upper seam, which, for a length of nearly 8 miles, varies from 100 to 130 ft. thick. Of this seam, 85 per cent is good coal. The seam dips to the north conformably with the shales, at angles of from 25° to 30°, and appears to have an uninterrupted dip for about 1.5 miles before being possibly cut o$&apos; by the northern hills. The coal-bearing shales extend east and west for a length of about 20 miles, but towards the east the continuity of the seams is broken by intrusive rocks. The coal is of the sub-bituminous variety, low in ash, bright in appearance, and breaks with a conchoidal fracture. It has the usual qualities of Tertiary coal-quick steam-raising and poor stacking-qualities. Pieces of resin, varying in size from

Apr 1, 1910

By K. Tangri, B. Swaroop

Simultaneous measurements of lattice (elastic) strain by X-ray line shift method and total strain with an electrical strain gage have been carried out on polycrystalli,ne nickel with the help of a specially designed tensometer attachment for the X-ray dif-fractometer. During the initial stages of deformation, the rate of increase in lattice strain closely follows the total strain until the plastic strain sets in. From then onwards, the two strains deviate from each other and with further increase in afiplied stress the rate of increase of lattice strain eventually decreases. Depending upon the mode of unloading, both compressive and tensile strains have been observed in nickel deformed up to 0.29 pct strain. These results have been explained on the basis of the effects of clustering of dislocations and also the production and behavior of point defects during loading and unloading, respectively. POLYCRYSTALS deformed plastically in a uniaxial tension test show residual lattice strains (hereafter referred to as RLS), which broaden the X-ray line profiles and shift their peak positions.&apos;&apos;4 It is known that uniform straining of a crystal lattice (macrostrain) produced movement of ddfraction line peaks, whereas nonuniform straining (microstrain) causes line broadening.= Though the nature and origin of RLS in deformed metals is not yet clearly understood, these are believed to be due to the presence of some form of a locked-up stress system. Several possible detailed interpretations6&apos;" of the stress system have been proposed by various workers and common to all these interpretations is the assumption that different parts of the aggregate have different tensile yield stresses; e.g., that a part A yields under a lower applied stress than a part B. Therefore, during the deformation process, the elastic strain in A will be less than that in B, and, after completion of deformation, B will tend to contract further than A but will be prevented from doing so by the restraining influence of A. Thus, when equilibrium is reached, A will be in compression while B is in tension. Although there is general agreement on the correctness of this argument, controversy still exists as to the exact nature of the parts A and B in a deformed metal. In an alternative approach to the creation of parts A and B, many other investigators have assumed that the RLS observed in unloaded specimens are in some way connected with the lack of proportionality between lattice strain and applied stress in the region above the yield stress." cullity13 has prepared a schematic summary of the results of previous workers, mainly Smith and Wood,2&apos;11 which suggests that, above the elastic limit, the lattice strain may increase less rapidly with respect to strain, or may even decrease with increase in applied stress. If the applied stress is then decreased, the lattice strain would decrease along a line parallel to the loading line in the elastic region and thus produce a compressive residual lattice strain after unloading. At equilibrium, to balance these compressive stresses? there would have to be regions under tensile stress which may well be the grain boundaries or the substructure walls formed during deformation. The present investigation was undertaken to gain a better understanding of the nature and origin of RLS and also to experimentally verify the salient features of this hypothesis. EXPERIMENTAL Stress and strain determinations were made with a specially constructed tensometer attachment for the X-ray diffractometer, Fig. 1: which permits the following measurements simultaneously on a sheet specimen under uniaxial tension at various stress levels during loading and unloading: a) lattice strains, E=. in a direction perpendicular to the direction of pulling (x direction) from shifts in X-ray line peak positions; b) the total strain, ex, in the direction of pulling. with the help of an electrical strain gage affixed to the back of the specimen directly below the area irradiated by X-rays: and c) the applied stress, with the help of a load cell which consisted of a calibrated stainless-steel sample of dimensions identical to those of the specimen under investigation, and to which it was coupled. Because of its high stacking fault energy.I4 nickel

Jan 1, 1970

By Robert E. Green, Robert A. Swanson

Ultrasonic attenuation and stress were measured simultaneously as a function of strain for aluminum single crystals tested in compression. The propagation mode and polarization of the ultrasonic waves were chosen with reference to the theoretical analysis presented in Part I. Good experimental agreement was found with this theory and with earlier experimental work in tensile tests. Support is given to the contention that ultrasonic -attenuation measurements are much more sensitive to the early stages of plastic deformation than are conventional stress -strain measurements. Dislocation meclzanisms are suggested which are compatible with both the present and the earlier experimental observations. A brief historical introduction of previous work concerned with the study of dislocation motion by ultrasonic-attenuation measurements has been given in Part I. The purpose of the present experimental investigation was to make use of the theoretical considerations from Part I in order to gain further knowledge concerning dislocation motions during plastic deformation. Emphasis was placed on the choice of propagation modes and polarization of the waves, such that interactions between these waves and dislocation movement on a specific slip system could be investigated. EXPERIMENTAL PROCEDURE Since the primary concern of this investigation was dislocation damping, other sources of damping were eliminated as much as possible. The test specimens were 0.5-in.-diam single crystals of 99.99+ pct pure aluminum grown from the melt by a modified Bridgman technique. Ultrasonic-attenuation measurements were made at a frequency of 10 megacycles per sec using a Style 56A001 Ultrasonic Attenuation Comparator manufactured by Sperry Products Inc. after a design by Chick, An- derson, and Truell.1 At this frequency the particle vibrations are essentially adiabatic and thermo-elastic damping should be absent. This frequency was selected since it was one of the frequencies used by Hikata et al.2 n conjunction with tensile tests on aluminum crystals, thus allowing direct comparison with this work. The use of quartz-crystal transducers insures that the amplitude of vibration is not sufficient to cause the break away of the dislocation loops from weak pinning points. The quartz-crystal transducers used all possessed a resonance frequency of 10 megacycles per sec and were thin circular discs 0.375 in. in diameter. X-cut crystals were used to generate the longitudinal waves and AC-cut crystals to generate the transverse waves. Aluminum was chosen as the basic material because it is a typical fcc metal whose deformation behavior is well-known and because the most recent work at the time the present research was initiated was that by Hikata et al. who used aluminum. The present tests were run in compression to see if such tests could be satisfactorily run in compression without being severely masked by grip effects.. A second reason was to compare the results in compression with those of the tension experiments of Hikata et at. Finally, shorter specimens could be run in compression with less over-all damping than in tension. All of the aluminum-crystal test specimens used were oriented for plastic deformation by single slip; i.e., they possessed the orientation having a maximum Schmid factor of 0.5. Because of the well-known time dependence 3 of plastic strain at constant stress, the test specimens were subjected to a quasi-static loading. Previous investigations4-&apos; have indicated that attenuation after plastic deformation is also time-dependent, so any continuous loading of the specimen would show that changes in attenuation were also a function of strain rate. By loading the specimen to a given stress level and holding it constant until the recovery process was essentially complete, the time dependence was eliminated. The quartz transducer was permanently bonded to the aluminum crystal using Eastman 910 cement. Excess cement was removed from around the quartz with DMF (dimethyl formamide). Eastman 910 was found to be far superior for bonding, especially with regard to the shear-wave transducer, since it formed a solid bond which readily supports shear-wave propagation. The solid bond formed by the Eastman 910 cement also insured that the quartz

Jan 1, 1964

By D. P. Pope, T. Vreeland

Observations of dislocations in zinc using Berg-Barrett X-ray micrography confirm the validity of a dislocation etch for (1010) surfaces. A technique for measurement of the depth in which dislocations can be imaged in X-ray micrographs is given. This depth on (0001) surfaces of zinc was found to be 2.5 µ using a (1013) reflection and CoKa radiation. BUCHANAN and Reed-Hill (B & RH) have recently questioned the ability of a dislocation etch to reveal all of the basal dislocations which intersect (1010) surfaces in annealed zinc crystals.&apos; This etch was developed by Brandt, Adams, and Vreeland who conducted a number of different experiments to check its ability to reveal dislocations.2,3 B & RH prepared (0001) foil specimens for transmission electron microscopy from annealed crystals and observed dislocation densities of about l08 cm per cu cm in the foils, while the etch indicated densities of the order of l04 cm per cu cm in their annealed crystals. As this etch has been used in a number of studies of dislocations in zinc, it is of considerable importance to reassess its validity in the light of the B & RH results. The X-ray work reported here was undertaken to check the ability of the etch to reveal dislocation intersections on (1070) surfaces of zinc. The X-ray technique was chosen for this check because it could be applied to the as-grown crystals with a relatively small amount of specimen preparation. We believe that the possibility of accidental deformation in preparation of the bulk specimens is considerably less than that for thin foil specimens suitable for transmission electron microscopy. Unfortunately, basal dislocations are not visible on Berg-Barrett topo-graphs of (1010) surfaces, which are the surfaces on which the etch is most effective. Therefore, a one-to-one correspondence between the etch and X-ray observations could not be made. Basal dislocations near (0001) surfaces have been observed by Schultz and Armstrong4 using the Berg-Barrett technique, but they did not report the as-grown dislocation density observed in their crystals. We have applied the X-ray technique in this study to surfaces oriented from 1 to 2 deg of the (0001) to determine the basal dislocation density, and have compared this density with that observed using the etch on a (1070) plane of the same crystal. The X-ray observations permit determination of the depth in which basal dislocations can be observed under the diffracting conditions used. SPECIMEN PREPARATION High purity zinc crystals are very soft, so a good deal of care must be exercised in the preparation of observation surfaces. As-grown crystals approximately 2.5 cm in diam and 20 cm long were acid cut into 1.25 cm cubes. A thin slab was cleaved from an (0001) surface to produce an accurately oriented reference surface on the specimen. Some of the cubes were examined in the as-machined condition while some were annealed in argon at 410°C for 2 hr. Heating and cooling rates were less than 2°C per min. Some of the specimens were scratched on a (0001) surface with a razor blade to produce fresh dislocations. Approximately 2 mm of material was acid lapped from one face of a cube to produce a surface oriented between 1 and 2 deg from the basal plane and parallel to the [1210] direction. A (1070) surface was also acid lapped. The lap used a 1 to 3 pct solution of HN03 in water to saturate a soft cloth which was backed by a stainless steel plate. The cloth was moved over the crystal surface at a rate of 20 cm per sec while a normal force of about 4 g was maintained between the cloth and the specimen. As-lapped surfaces were examined as were surfaces which were chemically and electrolytically polished after lapping. The small angle between a lapped surface and the (0001) plane was measured to 0.1 deg using a Unitron microgoniometer microscope (the cleaved surface was used as a reference in this measurement). The microscope was modified so that the intensity of reflected light could be continuously monitored on a meter. This modification produced nearly a ten-fold increase in the reproduceability of orientation readings. OBSERVATIONS The Unitron Microgoniometer observations indicated that the lapped surfaces had a terraced structure with the terraces quite rounded and spaced about 0.1 mm in the [1010] direction. The maximum change in slope between terraces was 0.25 deg, indicating a terrace height of about 0.1 µ. A Unitron measurement of the average angle between (0001) and a lapped surface was checked by micrometer measurement of the specimen and found to agree within 0.1 deg. The Berg-Barrett micrographs using (1013) reflections and CoKa radiation5 revealed subboundaries, short dislocation segments, spirals, and loops near the surfaces which were oriented from 1 to 2 deg of the (0001). Micrographs of surfaces prepared by lapping appeared very similar to those of the chemically and electrolytically polished surfaces. The loops and spirals were not extinct in (1013) or (0002) reflections, indicating that they have a nonbasal Burgers vector. Extinctions of the short, straight dislocations indicated that they belonged to an (0001)(1210) system. Fig. 1 is an example of a micrograph which shows a subboundary, and dislocation segments which are pre-

Jan 1, 1970

By David Cornell, D. L. Katz

Procedures for computing turbulent flow of gas in steady state near the well bore and a graphical method for predicting unsteady state laminar flow at distances from the well have been combined to compute pressure gradients in gas reservoirs. Methods are discussed for predicting single and multiple transients at constant flow rate in an infinite reservoir, predicting constant How rate. in a finite reservoir, reproducing and interpreting back pressure test data, and prediction of the behavior of a closed-in gas well. An example of the graphical method is given for a single transient and the results are compared to a published analytical solution. A typical calculation of the pressure gradient in a reservoir and the production of gas is made .starting with data from a hack pressure test. INTRODUCTION The calculation of pressure gradients throughouse a ga-reservoir at any point in its production history is a complex problem involving turbulent flow near the well bore and unsteady state flow of the gas from the reservoir. The problem is complicated further by the variety of boundary conditions that may be imposed upon the flow. Such boundary conditions include finite or infinite reservoirs. constant or variable rates of production, constant or varying bottom hole pressures, complex initial pressure distributions throughout the reservoir, and pressure maintenance through cycling. In addition to these problems there are the practical difficulties associated with natural gas reservoir analysis These might include: (1) variation. in the permeability and porosity throughout the formation. (2) variations in the thickness of the formation, (3) communication of the producing formation with other producing zones. (4) radial variations in permeability due to influx of drilling fluid. acidizing. or the buildup of liquid in the formation around the well, (5) partial penetration of the producing zone. (6) water flood, and many others. These problems will be considered eventually. In the mean- time, it is necessary to present methods of handling the case of radial flow through a homogeneous, regular, producing stratum to a single well uncomplicated by other factors. The idealized case of steady state, radial flow from a natural gas reservoir was studied by Elenbaas and Katz5 and by Mac-Koberts.&apos; An analysis of the unsteady flow of gases through porous media has been made by Aronofsky and Jenkins&apos; for the one dimensional laminar case with the boundary conditions of constant downstream pressure and uniform initial pressure. Solutions for the partial differential equation for unsteady state radial flow of liquids through porous media have been given by Van Everdingen and Hurst" for the constant bottom hole pressure and constant production rate cases for laminar flow in a reservoir initially at a constant pressure. The analogous heat transfer equation has been treated by Perry and Berggren9 for the case of quenching a cylindrical hole in an infinite medium to a constant temperature. The back pressure curve, which involves the variation of the bottom hole pressure as it is determined by the behavior of the reservoir as a whole. has been studied by Rawlins and Schellhardt,10 Binck-lev,&apos; Baumel and Breitung,&apos; and others. No complete. adequate treatment has been given for the unsteady state, radial flow of gases into a cylindrical hole from a porous medium with or without the presence of turbulent flow and for any set of boundary conditions. If one relies only on analytical solutions of the basic equations, a new solution must be obtained for each new boundary condition. Furthermore, the complexity of the mathematical expressions for boundary conditions other than the very simple cases limits the use of analytical solutions. Graphical methods exist, however. that are general in nature, accurate, and readily employed. The analysis of steady and unsteady, laminar and turbulent, radial flow for various boundary conditions with application to specific natural gas well problems by means of graphical procedures forms the content of this paper. STEADY STATE RADIAL FLOW EQUATION FOR LAMINAR AND TURBULENT FLOW A steady state radial flow equation for laminar and turbulent flow through unconsolidated sands has been given by Muskat as discussion of the work by Elenbaas and Katz.5 This equation is based on the properties of unconsolidated

Jan 1, 1953

By T. M. Morris

A SEARCH of the literature reveals that no measurements have been made of the forces acting between a small solid particle whose surface is hydrophobic, and an air bubble to which the solid adheres, both immersed in water. Analyses have been made of the forces acting to support a greased solid on the surface of water, and the forces acting to cause a solid, whose surface is hydrophobic, to adhere to an air bubble in water. The latter analysis T. M. MORRIS, Junior Member AIME, is in the Department of Metallurgical Engineering and Mineral Dressing, School of Mines and Metallurgy, Rolla, Mo. New York Meeting, February 1950. TP 2734 B. Discussion of this paper (2 copies) may be sent to Transactions AIME before Feb. 28, 1950. Manuscript received May 16, 1949. This paper is the result of work done for part of a doctor&apos;s thesis at the Missouri School of Mines and Metallurgy. is often incomplete, however, because the internal pressure of the bubble has been neglected. It will be demonstrated that the internal gas pressure is not a negligible factor when dealing with bubbles of the size encountered in flotation. A study of the forces acting between an air bubble attached to a large flat surface is informative. It must be borne in mind, however, that this is not the condition present in a flotation cell, where the particle is small compared to the size of the bubble. The bubble is allowed to spread to its maximum contact angle on a large flat surface in the first case, whereas in the second case, the spread of the bubble is limited to the surface of the small particle which is presented to the bubble. Kabanov and Frumkinl studied the forces acting to cause adhesion of bubbles of hydrogen to a large surface of mercury, which served as an electrode in a dilute sulphuric acid solution. The force acting to hold the bubble to the mercury surface was found to be the vertical component of the surface tension between hydrogen and the sulphuric acid solution. The forces tending to cause the bubble to separate from the mercury surface were found to be: (1) the force exerted due to the internal pressure of the bubble acting upon the area of contact between the bubble and the mercury surface, and (2) the buoyant force of the bubble minus the hydrostatic force acting at the base of the bubble. These investigators photographed bubbles that were just on the verge of separating from the mercury surface. From these photographs, they measured the contact angle between the mercury surface and the tangent to the hydrogen-solution interface at the point of contact between bubble and mercury surface. They calculated the volume of the bubble and the internal pressure of the bubble. The equivalence between the upward acting and downward acting forces was remarkable. Wark2 pursued an investigation similar to that of Kabanov and Frumkin, and at the same time. His deductions verified those of Kabanov and Frumkin. He also considered the conditions present in flotation and was aware of the effect of the internal pressure of the bubble. Further, he proposed several conditions under which a small solid particle would adhere to an air bubble in water. In 1922, Edser," an English physicist, made the following statement. "It must be remembered that no particle could float stably, but for the possibility of variation of the contact angle, for if this were a constant, a slight tilt would inevitably cause the particle to sink." Wark criticized this statement, maintaining that the contact angle does not vary. The experimental data to be presented indicates that Edser was correct. Experimental Procedure: Briefly, the experimental procedure was as follows. A bubble of air was generated in distilled water. A rod of known diameter, one end of which was water repellent, was attached to this bubble. The weight of the &apos;rod was measured. The internal pressure of the bubble was measured with a manometer. The hydrostatic head from the surface of the water to the bottom of the rod was measured. The angle between the horizontal projection of the end of the rod and the tangent to the bubble at the circle of contact be-

Jan 1, 1951

By T. M. Morris

A SEARCH of the literature reveals that no measurements have been made of the forces acting between a small solid particle whose surface is hydrophobic, and an air bubble to which the solid adheres, both immersed in water. Analyses have been made of the forces acting to support a greased solid on the surface of water, and the forces acting to cause a solid, whose surface is hydrophobic, to adhere to an air bubble in water. The latter analysis T. M. MORRIS, Junior Member AIME, is in the Department of Metallurgical Engineering and Mineral Dressing, School of Mines and Metallurgy, Rolla, Mo. New York Meeting, February 1950. TP 2734 B. Discussion of this paper (2 copies) may be sent to Transactions AIME before Feb. 28, 1950. Manuscript received May 16, 1949. This paper is the result of work done for part of a doctor&apos;s thesis at the Missouri School of Mines and Metallurgy. is often incomplete, however, because the internal pressure of the bubble has been neglected. It will be demonstrated that the internal gas pressure is not a negligible factor when dealing with bubbles of the size encountered in flotation. A study of the forces acting between an air bubble attached to a large flat surface is informative. It must be borne in mind, however, that this is not the condition present in a flotation cell, where the particle is small compared to the size of the bubble. The bubble is allowed to spread to its maximum contact angle on a large flat surface in the first case, whereas in the second case, the spread of the bubble is limited to the surface of the small particle which is presented to the bubble. Kabanov and Frumkinl studied the forces acting to cause adhesion of bubbles of hydrogen to a large surface of mercury, which served as an electrode in a dilute sulphuric acid solution. The force acting to hold the bubble to the mercury surface was found to be the vertical component of the surface tension between hydrogen and the sulphuric acid solution. The forces tending to cause the bubble to separate from the mercury surface were found to be: (1) the force exerted due to the internal pressure of the bubble acting upon the area of contact between the bubble and the mercury surface, and (2) the buoyant force of the bubble minus the hydrostatic force acting at the base of the bubble. These investigators photographed bubbles that were just on the verge of separating from the mercury surface. From these photographs, they measured the contact angle between the mercury surface and the tangent to the hydrogen-solution interface at the point of contact between bubble and mercury surface. They calculated the volume of the bubble and the internal pressure of the bubble. The equivalence between the upward acting and downward acting forces was remarkable. Wark2 pursued an investigation similar to that of Kabanov and Frumkin, and at the same time. His deductions verified those of Kabanov and Frumkin. He also considered the conditions present in flotation and was aware of the effect of the internal pressure of the bubble. Further, he proposed several conditions under which a small solid particle would adhere to an air bubble in water. In 1922, Edser," an English physicist, made the following statement. "It must be remembered that no particle could float stably, but for the possibility of variation of the contact angle, for if this were a constant, a slight tilt would inevitably cause the particle to sink." Wark criticized this statement, maintaining that the contact angle does not vary. The experimental data to be presented indicates that Edser was correct. Experimental Procedure: Briefly, the experimental procedure was as follows. A bubble of air was generated in distilled water. A rod of known diameter, one end of which was water repellent, was attached to this bubble. The weight of the &apos;rod was measured. The internal pressure of the bubble was measured with a manometer. The hydrostatic head from the surface of the water to the bottom of the rod was measured. The angle between the horizontal projection of the end of the rod and the tangent to the bubble at the circle of contact be-

Jan 1, 1951

By H. Margolin, E. Ence

In order to understand the effect of zirconium on properties of Ti-Cu-A1 alloys, Ti-Zr alloys were examined for the presence of ordering or compounds at the following compositions in weight percent: 24.1 pct Zr (lZr:GTi), 32.2 pct Zr (lZr:4Ti), 38.8 pct Zr (lZr:3Ti), 49.0 pct Zr(1Zr:ZTi). Alloys were prepared as 15-g buttons by non- consumable arc melting under argon atmosphere from Bureau of Mines titanium (Bhn 63) and Reactor Grade zirconium (Bhn 150). Weight losses during melting did not exceed 1 pct of the initial button weight. Prior to heat treatment, buttons were hot-rolled at 600" to 700°C to rods of about 6 mm diam. Contamination after hot-rolling was found to extend to a depth of less than 0.5 mm. Specimens for heat treatment were wrapped in molybdenum sheet, annealed in argon-filled quartz capsules, and quenched by breaking the capsules under iced brine. Annealing times were as follows: 700°C — 7 days; 600°C— 14 days; 575°C-1 and 2 months; 525°C-2 months; 500°C-2 months. Prior to heat treatment, all Ti-Zr alloys were vacuum annealed at 900°C to remove hydrogen. The reanneal of 575°C specimens for an additional month produced no observable microstructure changes. The results obtained by microstructure and X-ray diffraction are shown in Fig. 1, together with data of Hayes et al.&apos; No other phases than a or P were found. Small amounts of retained P were detected by X-ray in the 49 pct Zr alloy. The data of the present investigation suggests that ß and a transus boundaries are at considerably lower temperatures than those of Hayes et al. The work of Hayes et al. is based on sponge titanium and Bureau of Mines zirconium, both of which contained 0.15 pct 0. Since melting was performed in

Jan 1, 1962

By Richard E. Chism

The metric system is now in official use in the Republic of Mexico, having been adopted by the Government in the year 1862. Athough it is used to compute all customs and other duties to be paid to the General Government, in the measurement of public and private lands arid in all freight and other transactions on the railroads, and is taught exclusively in the public schools, the system has made but slight head way among the people,and has not succeeded in displacing the old-time weights and measures, which are still used in ordinary commerce. The latter were founded on old Spanish models, but, owing to the inexactness of the first standards and to subsequent changes, differ at present very widely from their originals. As to local modifications, weights are the same all over the Republic, but measures of the same name differ greatly in capacity in different States, and even in neighboring towns. The value in the metric system here assigned to each denomination of the old weights and measures is that fixed by the Mexican Government at the time of the adoption of the metric system. The equivalents in American weights and measures were calculated by me from data found in Trautwine&apos;s Pocket-Book as to the comparison between the French and American weights and measures, and are believed to be correct. I shall be thankful for early notice of any error that may be detected, that it may be corrected before the final publication of this paper in the Transactions. Linear Measures. Kilometers. Miles. 1 legua (league) = 5000 varas . = 4.19 2.604375 Meters. Feet. 1 vara (yard) = 3 pies.....= 0.83800 2.749578 1 pie (foot) = 12 pulgadas.....=0.27933 0.916526 Inches. 1 pulgada (inch) = 12 lineas . = 0.02328 0.916526 1 linea (line).......= 0.00194 0.076577 The vara is also divided (for dry-goods-selling) into palms or cuartas (palms or quarters). Meters. Feet. Inches. 1 palmo or cuarta .. .. = 0.209500 =0.687394 = 8.248728

Jan 1, 1887

By W. L. DeMoulin

A rather detailed description of the entire plant and leaching process was given in a paper recently presented to the Institute,I so this paper will cover briefly only the crushing practice of the New Cornelia Copper Co. for the year 1918. The ore, which is mined by steam shovels and loaded in side-dump cars, passes through two crushing plants. These crushing plants were constructed to crush the ore required by a leaching plant of 5000 tons daily capacity, during a crushing period of 16 hours. The primary plant reduces to less than 3 in. (76 mm.) and the secondary plant, to 1/4 in. (6.35 mm.), which is sufficiently fine for satisfactory percolation of solution through the ore in the leaching tanks, and to give-good extraction. The ore is then conveyed to the leaching tanks by a system of 28-in. (71-cm.) belt conveyors. On the way to the leaching tanks, it passes through an automatic sampling plant, where a 1-per cent. sample is taken. From the primary crushing plant, the ore is conveyed by two 36-in. (91-cm.) belt conveyors to a 10,000-ton steel storage bin, with a reinforced-concrete flat bottom. The ore discharges from the bottom of this&apos; bin onto four 20-in. belt conveyors, which deliver it to the four units of crushers in the secondary crushing plant. There is no storage bin between the mine and the primary crushing plant. The ore breaks very coarse, is very hard, and contains a great many boulders, some as large as 4 1/2 by 4 1/2 by 10 ft. (1.3 by 1.3 by 3 m.). Jams form in the bowl of the coarse crusher in the primary crushing plant, as a consequence, and are freed by means of an immense steel hook operated from a 40-ton electric traveling crane. Primary Crushing Plant The primary plant consists of one No. 24 Gates, style K, gyratory crusher, followed by four Gates No. 8, style K, gyratory crushers. All

Jan 1, 1920

By Henry Howe

1. Introduction.-This paper is based in large part on the examination of two rings, shown in section in Fig. 4 to 15, cut from an eroded 14-in. (35.56-cm.) gun, liner, and containing, according to Booth, Garrett, & Blair: Carbon, 0.380 per cent.; manganese, 0.655 per cent.; nickel, 2.810 per cent.; vanadium, 0; chromium, a few hundredths of 1 per cent.; tungsten, 0; molybdenum, 0. These rings were received from Admiral Joseph Strauss, then Chief of Ordnance, U. S. Navy, through the kindness of Mr. Hudson Maxim, Chairman of the Committee on Ordnance and Explosives,, of the U. S. Naval Consulting Board.

Jan 2, 1918

By William T. Barrett, James E. Lawver, James L. Wright

One of the problems facing both the designer and the user of magnetic separators is the evaluation of the body forces acting on particles in the magnetic field of the separator. Perhaps the most elegant method of evaluating the body force associated with a drum-type magnetic separator is that recently suggested by W. F. Brown.&apos; Brown measures the radial component of the field intensity 1/2 in. from the drum surface and fits a Fourier series in the angle about the drum axis (Fig. 1). Once the coefficients of the series are known, it is then possible to calculate the values of the radial and angular

Jan 1, 1971

By R. S. Dean

JUST as the mineralogical name bauxite has come to include several minerals not known at the time the name was first applied, so the concept of bauxite as the one source of alumina must be enlarged during the war period to include the production of alumina from other, low-grade sources. Speaking in a narrow mineral logical sense, there is no such thing as bauxite, and similarly there is now no one source of alumina, and no one process for its extraction.

Jan 1, 1943

By John Dasher

Extrapolation is a useful technique, but it can be overdone. Seldom is it justified to study over a range of 1 to 6 and extrapolate the results to 150,000. It is especially dangerous if the extrapolation is based on a false assumption. The authors assume settlers scale-up by residence time rather than by area, admit their result (a settler depth of 7 m) is "unreasonable" and suggest longer, wider, shallower settlers might be better. Various authors have noted for a copper-LIX system a total flow basis of 2 gpm per sq ft for sizing settlers. The results of this are compared with those in the paper in [Table 7]. The authors note that flooding of their settlers was never approached. Thus the smallest unit calculated is understandably twice too big. The largest however, is 5% of the required size. I note that the figures in [Table 6] for 1/min/cm2 are based on plan area rather than cross section as titled and are wrong by l0 4. A flow of 2050 1/min/cm2 is about Mach I. It is also 10 5/3 or 46.5 times that of the little one, although the abstract says the design was based on constant flow rate per unit cross section.

Jan 1, 1977